Gradient-Normalized Smoothness for Optimization with Approximate Hessians | Paper Citation Record

Observation 33cc48c2-fc97-411a-831c-11bb3deae0d8 · outbound

This paper cites Inexact tensor methods and their application to stochastic convex optimization.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Inexact tensor methods and their application to stochastic convex optimization

Reference 1

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This paper cites Rethinking Gauss-Newton for learning over-parameterized models.Advances in neural information processing systems, 36:33379– 33402, 2023.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Rethinking Gauss-Newton for learning over-parameterized models.Advances in neural information processing systems, 36:33379– 33402, 2023

Reference 2

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This paper cites Gradient descent converges linearly for logistic regression on separable data.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Gradient descent converges linearly for logistic regression on separable data

Reference 3

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This paper cites Self-concordant analysis for logistic regression.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Self-concordant analysis for logistic regression

Reference 4

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Observation c4d6a485-c5c2-4038-be2b-95f1662de287 · outbound

This paper cites A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications.Mathematics of Operations Research, 42(2):330–348, 2017.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications.Mathematics of Operations Research, 42(2):330–348, 2017

Reference 5

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This paper cites Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models.Mathematical Programming, 163:359–368, 2017.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models.Mathematical Programming, 163:359–368, 2017

Reference 6

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This paper cites Optimal and adaptive Monteiro-Svaiter acceleration.Advances in Neural Information Processing Systems, 35:20338–20350, 2022.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Optimal and adaptive Monteiro-Svaiter acceleration.Advances in Neural Information Processing Systems, 35:20338–20350, 2022

Reference 7

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Observation 000cc47f-f6c0-4c66-8e00-20f02e431960 · outbound

This paper cites Acceleration with a ball optimization oracle.Advances in Neural Information Processing Systems, 33:19052–19063, 2020.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Acceleration with a ball optimization oracle.Advances in Neural Information Processing Systems, 33:19052–19063, 2020

Reference 8

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Observation b8b411f2-b4fd-4998-afc8-5f12144d098c · outbound

This paper cites Adaptive cubic regularisation methods for unconstrained optimization.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Adaptive cubic regularisation methods for unconstrained optimization

Reference 9

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Observation 89bdded2-26cc-4a0d-b636-19dc897edf42 · outbound

This paper cites Adaptive cubic regularisation methods for unconstrained optimization.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Adaptive cubic regularisation methods for unconstrained optimization

Reference 10

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Observation 1e15c26d-3c8b-4a70-8a17-0281fcb199c6 · outbound

This paper cites On the oracle complexity of first- order and derivative-free algorithms for smooth nonconvex minimization.SIAM Journal on Optimization, 22(1):66–86, 2012.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians On the oracle complexity of first- order and derivative-free algorithms for smooth nonconvex minimization.SIAM Journal on Optimization, 22(1):66–86, 2012

Reference 11

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Observation 5964b363-c63e-4039-94ad-b8aa54ba5c77 · outbound

This paper cites Gould, and Philippe L.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Gould, and Philippe L

Reference 12

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Observation ac04ab4a-f928-4916-bb07-e52d258b301f · outbound

This paper cites Universal regularization methods: varying the power, the smoothness and the accuracy.SIAM Journal on Optimization, 29(1):595– 615, 2019.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Universal regularization methods: varying the power, the smoothness and the accuracy.SIAM Journal on Optimization, 29(1):595– 615, 2019

Reference 13

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Observation ea8edd39-f06d-4404-ab00-2324f8d94c1c · outbound

This paper cites Global convergence rate analysis of unconstrained optimization methods based on probabilistic models.Mathematical Programming, 169:337– 375, 2018.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Global convergence rate analysis of unconstrained optimization methods based on probabilistic models.Mathematical Programming, 169:337– 375, 2018

Reference 14

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Observation 3e4b9eba-daa4-4eb6-83bf-99d902a421de · outbound

This paper cites Libsvm: A library for support vector machines.ACM Trans.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Libsvm: A library for support vector machines.ACM Trans

Reference 15

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Observation ad5a9d35-63b3-49f7-a88f-8c82c1eca75c · outbound

This paper cites Unified Convergence Theory of Stochastic and Variance-Reduced Cubic Newton Methods.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Unified Convergence Theory of Stochastic and Variance-Reduced Cubic Newton Methods

Reference 16

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Observation 3fd22ec8-858a-4aac-b011-0431e940399d · outbound

This paper cites SIAM, 2000.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians SIAM, 2000

Reference 17

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Observation 3cf995c8-428b-42df-b391-e3d88e810f99 · outbound

This paper cites Quasi-Newton methods, motivation and theory.SIAM review, 19(1):46–89, 1977.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Quasi-Newton methods, motivation and theory.SIAM review, 19(1):46–89, 1977

Reference 18

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Observation 29d90483-c6af-4890-aa45-26ce01e5dd62 · outbound

This paper cites Minimizing Quasi-Self-Concordant Functions by Gradient Regularization of Newton Method.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Minimizing Quasi-Self-Concordant Functions by Gradient Regularization of Newton Method

Reference 19

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Observation 26aab011-cf16-4d3f-bc75-8cf48d3f8a26 · outbound

This paper cites First and zeroth-order implementations of the regularized Newton method with lazy approximated hessians.Journal of Scientific Computing, 103(1):32, 2025.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians First and zeroth-order implementations of the regularized Newton method with lazy approximated hessians.Journal of Scientific Computing, 103(1):32, 2025

Reference 20

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Observation c8f84695-ee68-4e91-b2c3-f6d52ffa1eeb · outbound

This paper cites Super-universal regularized Newton method.SIAM Journal on Optimization, 34(1):27–56, 2024.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Super-universal regularized Newton method.SIAM Journal on Optimization, 34(1):27–56, 2024

Reference 21

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Observation 816d381e-1e3b-4030-98d5-953bf7f797b3 · outbound

This paper cites Minimizing uniformly convex functions by cubic regulariza- tion of Newton method.Journal of Optimization Theory and Applications, 189(1):317–339, 2021.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Minimizing uniformly convex functions by cubic regulariza- tion of Newton method.Journal of Optimization Theory and Applications, 189(1):317–339, 2021

Reference 22

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Observation c6f69551-9a40-4a2e-8875-53c9cd892b4d · outbound

This paper cites Gradient regularization of Newton method with Bregman distances.Mathematical Programming, pages 1–25, 2023.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Gradient regularization of Newton method with Bregman distances.Mathematical Programming, pages 1–25, 2023

Reference 23

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Observation f3f0aa94-f402-46f3-95c5-52a1d3080c88 · outbound

This paper cites Polynomial preconditioning for gradient methods, 2023.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Polynomial preconditioning for gradient methods, 2023

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Observation d13ee338-2a1c-4789-b70a-cf8b2fe8a14b · outbound

This paper cites Spectral preconditioning for gradient methods on graded non-convex functions.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Spectral preconditioning for gradient methods on graded non-convex functions

Reference 25

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Observation abd4e59a-489a-43ab-b829-850b1c09fd57 · outbound

This paper cites Sharp analysis of stochastic optimization under global Kurdyka-Lojasiewicz inequality.Advances in Neural Information Processing Systems, 35:15836–15848, 2022.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Sharp analysis of stochastic optimization under global Kurdyka-Lojasiewicz inequality.Advances in Neural Information Processing Systems, 35:15836–15848, 2022

Reference 26

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Observation 3e3ab534-e3ae-4f2b-a647-a9afe459ee6a · outbound

This paper cites M-fac: Efficient matrix-free approximations of second-order information.Advances in Neural Information Processing Systems, 34:14873– 14886, 2021.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians M-fac: Efficient matrix-free approximations of second-order information.Advances in Neural Information Processing Systems, 34:14873– 14886, 2021

Reference 27

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Observation 842828d5-33f6-4255-a409-ef3ae15ff672 · outbound

This paper cites Randomized subspace regularized Newton method for unconstrained non-convex optimization.arXiv preprint arXiv:2209.04170, 2022.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Randomized subspace regularized Newton method for unconstrained non-convex optimization.arXiv preprint arXiv:2209.04170, 2022

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Observation b97c589f-50c7-4d4b-8b82-dba8b1c38848 · outbound

This paper cites Methods for Convex $(L_0,L_1)$-Smooth Optimization: Clipping, Acceleration, and Adaptivity.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Methods for Convex $(L_0,L_1)$-Smooth Optimization: Clipping, Acceleration, and Adaptivity

Reference 29

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Observation 885aa9b0-22d3-4ba7-9921-cba30e344a52 · outbound

This paper cites Rsn: randomized subspace Newton.Advances in Neural Information Processing Systems, 32, 2019.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Rsn: randomized subspace Newton.Advances in Neural Information Processing Systems, 32, 2019

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Observation ad4c9556-8068-4734-ad0a-6a97517cb7bc · outbound

This paper cites A cubic regularization of newton’s method with finite difference hessian approximations.Numerical Algorithms, pages 1–24, 2022.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians A cubic regularization of newton’s method with finite difference hessian approximations.Numerical Algorithms, pages 1–24, 2022

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Observation 3cd5eb52-bdbb-4abd-8ea9-e85a182015ce · outbound

This paper cites On inexact solution of auxiliary problems in tensor methods for convex optimization.Optimization Methods and Software, 36(1):145–170, 2021.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians On inexact solution of auxiliary problems in tensor methods for convex optimization.Optimization Methods and Software, 36(1):145–170, 2021

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Observation 998dcdc1-687d-4d7d-9f3c-f359ee471c4b · outbound

This paper cites A Fast Newton Method Under Local Lipschitz Smoothness.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians A Fast Newton Method Under Local Lipschitz Smoothness

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Resolution: verified exact; local_arxiv, observed 2026-08-15T20:05:23.999283Z

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Observation 28cce406-c302-48cd-8b7c-e52e75260a12 · outbound

This paper cites The modification of Newton’s method for unconstrained optimization by bounding cubic terms.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians The modification of Newton’s method for unconstrained optimization by bounding cubic terms

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Observation b04b39b5-4bd4-44c1-b8c6-6a9da5d81efb · outbound

This paper cites On Nesterov’s nonsmooth Chebyshev–Rosenbrock functions.Nonlinear Analysis: Theory, Methods & Applications, 75(3):1282–1289, 2012.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians On Nesterov’s nonsmooth Chebyshev–Rosenbrock functions.Nonlinear Analysis: Theory, Methods & Applications, 75(3):1282–1289, 2012

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Gradient-Normalized Smoothness for Optimization with Approximate Hessians Unresolved cited work

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Observation d4e3a2f7-1102-44e6-930d-8d607673bc47 · outbound

This paper cites Sketch-and-project meets Newton method: Global O(1/kˆ2) convergence with low-rank updates.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Sketch-and-project meets Newton method: Global O(1/kˆ2) convergence with low-rank updates

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Observation 151b1704-b32a-41d0-995a-c22513008778 · outbound

This paper cites Newton Method Revisited: Global Convergence Rates up to $\mathcal {O}\left(k^{-3} \right)$ for Stepsize Schedules and Linesearch Procedures.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Newton Method Revisited: Global Convergence Rates up to $\mathcal {O}\left(k^{-3} \right)$ for Stepsize Schedules and Linesearch Procedures

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Observation ec8d624e-76d3-483b-bfb0-a2499b137973 · outbound

This paper cites On Nesterov’s smooth Chebyshev–Rosenbrock function.Optimization Methods & Software, iFirst, 12 2011.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians On Nesterov’s smooth Chebyshev–Rosenbrock function.Optimization Methods & Software, iFirst, 12 2011

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Observation 184c69bc-a4a8-4624-936f-f7f893e8d494 · outbound

This paper cites Beyond nonconvexity: A universal trust-region method with new analyses.arXiv e-prints, pages arXiv–2311, 2023.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Beyond nonconvexity: A universal trust-region method with new analyses.arXiv e-prints, pages arXiv–2311, 2023

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Observation 37893271-1d19-4f92-9637-039828b9bc14 · outbound

This paper cites Non-asymptotic Global Convergence Analysis of BFGS with the Armijo-Wolfe Line Search.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Non-asymptotic Global Convergence Analysis of BFGS with the Armijo-Wolfe Line Search

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Observation 418ae7f7-477f-4a8c-98fc-40b94aa6eb03 · outbound

This paper cites Non-asymptotic superlinear convergence of standard quasi- Newton methods.Mathematical Programming, 200(1):425–473, 2023.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Non-asymptotic superlinear convergence of standard quasi- Newton methods.Mathematical Programming, 200(1):425–473, 2023

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Observation 0def4ffa-5026-403c-a240-ac8370a3c11c · outbound

This paper cites Spinger, 2006.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Spinger, 2006

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Observation 2a77cb49-0d5a-4b6a-acc8-1a3b53a91272 · outbound

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Gradient-Normalized Smoothness for Optimization with Approximate Hessians Moreau envelope and proximal-point methods under the lens of high-order regularization, 2025

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.615431Z

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Observation 47e0f25d-80a1-4a67-a690-fdadb5bd9eb5 · outbound

This paper cites Cubic Regularization is the Key! The First Accelerated Quasi-Newton Method with a Global Convergence Rate of $O(k^{-2})$ for Convex Functions.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Cubic Regularization is the Key! The First Accelerated Quasi-Newton Method with a Global Convergence Rate of $O(k^{-2})$ for Convex Functions

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Observation a59f42a5-c1b4-41e0-9f19-cb2339d993ac · outbound

This paper cites Global linear convergence of Newton's method without strong-convexity or Lipschitz gradients.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Global linear convergence of Newton's method without strong-convexity or Lipschitz gradients

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Observation ac818394-5c91-47c2-89e5-f0629df8c8f2 · outbound

This paper cites Revisiting gradient clipping: Stochastic bias and tight convergence guarantees.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Revisiting gradient clipping: Stochastic bias and tight convergence guarantees

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Observation 706a6e74-544c-46a0-8a49-8a9152e3524e · outbound

This paper cites Limitations of the empirical fisher approximation for natural gradient descent.Advances in neural information processing systems, 32, 2019.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Limitations of the empirical fisher approximation for natural gradient descent.Advances in neural information processing systems, 32, 2019

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Observation 7d8990e0-2b76-4620-b9fe-64cbda07a7f8 · outbound

This paper cites Anisotropic proximal gradient.Mathematical Pro- gramming, pages 1–45, 2025.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Anisotropic proximal gradient.Mathematical Pro- gramming, pages 1–45, 2025

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.584997Z

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Observation 4b257ac7-0fe7-4776-96a0-1d4ce3bd40b0 · outbound

This paper cites Convex and non- convex optimization under generalized smoothness.Advances in Neural Information Processing Systems, 36:40238–40271, 2023.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Convex and non- convex optimization under generalized smoothness.Advances in Neural Information Processing Systems, 36:40238–40271, 2023

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.571899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f004eb03-5232-4988-859a-86a2ea23f883 · outbound

This paper cites Relatively smooth convex optimization by first-order methods, and applications.SIAM Journal on Optimization, 28(1):333–354, 2018.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Relatively smooth convex optimization by first-order methods, and applications.SIAM Journal on Optimization, 28(1):333–354, 2018

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.687961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99295052-3810-4e3d-b49b-a398093292cf · outbound

This paper cites Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization

Reference 52

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:05:23.928393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d2f1a6da-890b-4ed9-ae78-3a6c577a91f5 · outbound

This paper cites New insights and perspectives on the natural gradient method.Journal of Machine Learning Research, 21(146):1–76, 2020.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians New insights and perspectives on the natural gradient method.Journal of Machine Learning Research, 21(146):1–76, 2020

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.695482Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6ce282d-22d7-45e4-9c5a-4c26f237e0b2 · outbound

This paper cites Inverting modified matrices.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Inverting modified matrices

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.541000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 66c9b4f1-b18b-407d-b11e-e8862aab8891 · outbound

This paper cites Regularized Newton method with globalO(1/k2) convergence.SIAM Journal on Optimization, 33(3):1440–1462, 2023.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Regularized Newton method with globalO(1/k2) convergence.SIAM Journal on Optimization, 33(3):1440–1462, 2023

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.527859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 64b7875b-47ea-4e79-8b3c-982d12260190 · outbound

This paper cites Problem complexity and method efficiency in optimization.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Problem complexity and method efficiency in optimization

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.514377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 809bc7a0-6af9-4a31-a48a-7af768e720f3 · outbound

This paper cites Modified Gauss–Newton scheme with worst case guarantees for global perfor- mance.Optimisation methods and software, 22(3):469–483, 2007.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Modified Gauss–Newton scheme with worst case guarantees for global perfor- mance.Optimisation methods and software, 22(3):469–483, 2007

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.499738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5bda79ba-60ad-480d-8318-6eacfbd8f95a · outbound

This paper cites Universal gradient methods for convex optimization problems.Mathematical Programming, 152(1):381–404, 2015.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Universal gradient methods for convex optimization problems.Mathematical Programming, 152(1):381–404, 2015

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.484464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1f197504-1d29-4b6f-811a-8c23079772df · outbound

This paper cites Springer, 2018.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Springer, 2018

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.713553Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c98357e-7c2b-4232-b96f-7365f6c90ede · outbound

This paper cites Implementable tensor methods in unconstrained convex optimization.Mathe- matical Programming, 186:157–183, 2021.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Implementable tensor methods in unconstrained convex optimization.Mathe- matical Programming, 186:157–183, 2021

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.456643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation adb9b673-a760-45d2-8bb1-e54a4d377afd · outbound

This paper cites Superfast second-order methods for unconstrained convex optimization.Journal of Optimization Theory and Applications, 191:1–30, 2021.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Superfast second-order methods for unconstrained convex optimization.Journal of Optimization Theory and Applications, 191:1–30, 2021

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.720205Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00435c1b-d5c6-45e3-9e3f-37b8784883c9 · outbound

This paper cites Primal subgradient methods with predefined step sizes.Journal of Optimization Theory and Applications, pages 1–33, 2024.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Primal subgradient methods with predefined step sizes.Journal of Optimization Theory and Applications, pages 1–33, 2024

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.432848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7fa613a7-c7d2-4906-9be5-5417075c675b · outbound

This paper cites SIAM, 1994.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians SIAM, 1994

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.420120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a3c5ea79-44b4-4b42-a6dd-4587c6aa78b4 · outbound

This paper cites Cubic regularization of newton method and its global performance.Mathematical programming, 108(1):177–205, 2006.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Cubic regularization of newton method and its global performance.Mathematical programming, 108(1):177–205, 2006

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.407556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 665e95a8-9326-450d-af9d-4c73f54d11fa · outbound

This paper cites Newton’s method and its use in optimization.European Journal of Operational Research, 181(3):1086–1096, 2007.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Newton’s method and its use in optimization.European Journal of Operational Research, 181(3):1086–1096, 2007

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.395527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b38381f3-fb85-42f2-b1c2-3644893684c1 · outbound

This paper cites Regularized Newton method for unconstrained convex optimization.Mathe- matical programming, 120:125–145, 2009.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Regularized Newton method for unconstrained convex optimization.Mathe- matical programming, 120:125–145, 2009

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.383839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 479aab8e-0ba1-4780-b61e-343c81d6f491 · outbound

This paper cites PhD thesis, PhD thesis, UCL-Université Catholique de Louvain, 2022.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians PhD thesis, PhD thesis, UCL-Université Catholique de Louvain, 2022

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.373452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9500750d-9f8f-41d5-9d83-28c156b597b1 · outbound

This paper cites Global Complexity Analysis of BFGS.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Global Complexity Analysis of BFGS

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.745471Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation edf18fd0-f604-4766-94d4-b0bdd046f595 · outbound

This paper cites New results on superlinear convergence of classical quasi-Newton methods.Journal of optimization theory and applications, 188:744–769, 2021.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians New results on superlinear convergence of classical quasi-Newton methods.Journal of optimization theory and applications, 188:744–769, 2021

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.361785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e4acfd59-36bd-47b7-a958-c5f484a213ad · outbound

This paper cites an unresolved cited work.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Unresolved cited work

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.753125Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c49a54a8-738d-434d-a26c-b29e9441da2f · outbound

This paper cites Adaptive quasi-Newton and Anderson acceleration framework with explicit global (accelerated) convergence rates.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Adaptive quasi-Newton and Anderson acceleration framework with explicit global (accelerated) convergence rates

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.343571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 67f255c9-f7db-4819-acd7-5a690b6f8e2d · outbound

This paper cites Generalized self-concordant functions: A recipe for newton-type methods, 2018.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Generalized self-concordant functions: A recipe for newton-type methods, 2018

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.331616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 596c37ec-7556-4be7-847c-315070f1c195 · outbound

This paper cites Toward a Unified Theory of Gradient Descent under Generalized Smoothness.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Toward a Unified Theory of Gradient Descent under Generalized Smoothness

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.764428Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c40df07-6873-486d-9c4e-09933ada79a3 · outbound

This paper cites Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Optimizing $(L_0, L_1)$-Smooth Functions by Gradient Methods

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.768307Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca009f8c-eacd-44c0-969e-2f91c5c52562 · outbound

This paper cites Trust region methods for nonconvex stochastic optimization beyond Lipschitz smoothness.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Trust region methods for nonconvex stochastic optimization beyond Lipschitz smoothness

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.320616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation df8ccd36-637d-4762-b6b6-a52df8e35d6c · outbound

This paper cites Preconditioned gradient descent for over- parameterized nonconvex Burer–Monteiro factorization with global optimality certification.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Preconditioned gradient descent for over- parameterized nonconvex Burer–Monteiro factorization with global optimality certification

Reference 76

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.308797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d1d151ed-d62c-4dfb-bcc9-1b5be8b4d84e · outbound

This paper cites Why gradient clipping accelerates training: A theoretical justification for adaptivity.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Why gradient clipping accelerates training: A theoretical justification for adaptivity

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-15T20:05:23.778640Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 175b6bea-5215-4ede-854e-0d7ef9459758 · outbound

This paper cites Cubic regularized subspace Newton for non- convex optimization.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Cubic regularized subspace Newton for non- convex optimization

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.298040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation fa7d9d8b-5bc9-4488-bd1f-fbe92e34178a · outbound

This paper cites SearchorExact Newton:stands for the partial case of Algorithm 1 using our adaptive search procedure (16), andH(x)≡∇ 2f(x).

Gradient-Normalized Smoothness for Optimization with Approximate Hessians SearchorExact Newton:stands for the partial case of Algorithm 1 using our adaptive search procedure (16), andH(x)≡∇ 2f(x)

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.287345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d9d3ff7b-4fe1-41bf-b536-47714b9855c7 · outbound

This paper cites SearchorWeighted Gauss-Newton:refers to the variant of Algo- rithm 1 with Hessian approximation of the form (13) or (19), combined with our adaptive search (16).

Gradient-Normalized Smoothness for Optimization with Approximate Hessians SearchorWeighted Gauss-Newton:refers to the variant of Algo- rithm 1 with Hessian approximation of the form (13) or (19), combined with our adaptive search (16)

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.276445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 618af6b0-11de-41f3-8c9d-d0e72e6a484f · outbound

This paper cites Search,γk = 1 Mk :denotes the Gradient-Regularized Newton Method with adaptive search as in [21], usingγk := 1 Mk andMk is chosen to satisfy the condition (17).

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Search,γk = 1 Mk :denotes the Gradient-Regularized Newton Method with adaptive search as in [21], usingγk := 1 Mk andMk is chosen to satisfy the condition (17)

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.265774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2a43c2fc-0b53-47da-9bd1-0086297add24 · outbound

This paper cites Search,γk = ∥∇f(x k)∥∗ Mk :denotes the Gradient-Regularized Newton Method with adaptive search as in [21], usingγk := ∥∇f(xk)∥∗ Mk andMk is chosen to satisfy the condition (17).

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Search,γk = ∥∇f(x k)∥∗ Mk :denotes the Gradient-Regularized Newton Method with adaptive search as in [21], usingγk := ∥∇f(xk)∥∗ Mk andMk is chosen to satisfy the condition (17)

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.254120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 18406e58-8b82-428f-bb4a-e1460d19d51a · outbound

This paper cites an unresolved cited work.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Unresolved cited work

Reference 83

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:05:24.241986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 995902f1-dcab-440c-892a-c56665bc8f59 · outbound

This paper cites To demonstrate that our theoretical findings are reflected in practice, we validate the effects observed in (Fig.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians To demonstrate that our theoretical findings are reflected in practice, we validate the effects observed in (Fig

Reference 84

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T20:05:24.231911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a1fa0185-f8a2-4b33-9fac-6478c1fd100a · outbound

This paper cites an unresolved cited work.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Unresolved cited work

Reference 85

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:05:24.221559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d20d16cd-3cc4-484a-b45a-84b0ebd9042b · outbound

This paper cites In our experiments, we extend the Nesterov-Chebyshev-Rosenbrock function to (24).

Gradient-Normalized Smoothness for Optimization with Approximate Hessians In our experiments, we extend the Nesterov-Chebyshev-Rosenbrock function to (24)

Reference 86

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T20:05:24.209671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ebe75389-d0d0-4c6f-8725-8cbedcfe4225 · outbound

This paper cites Note that when operator u(·) is linear, H(x) is the exact Hessian.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Note that when operator u(·) is linear, H(x) is the exact Hessian

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.197318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0cdd2b33-6bab-4d2d-90d5-d5466b8744a6 · outbound

This paper cites an unresolved cited work.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Unresolved cited work

Reference 88

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:05:24.185779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 428200a2-d098-4952-bb70-dc3044260788 · outbound

This paper cites Repeating the reasoning from the previous case, it follows immediately that ∥∇2f(x)−H(x)∥ ≤ ξ0 + ξ1√µ ∥∇f(x)∥∗, which is the required bound.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Repeating the reasoning from the previous case, it follows immediately that ∥∇2f(x)−H(x)∥ ≤ ξ0 + ξ1√µ ∥∇f(x)∥∗, which is the required bound

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.174482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d3aaef5e-6ec2-4aaf-a612-c62c280efb15 · outbound

This paper cites (71) Note that it resembles a combination of the Gauss-Newton and Fisher approximation matrices, and forp= 2 it gives the classic Gauss-Newton approximation.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians (71) Note that it resembles a combination of the Gauss-Newton and Fisher approximation matrices, and forp= 2 it gives the classic Gauss-Newton approximation

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.161469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6f314b71-89bd-4a70-a096-415ae87e85c7 · outbound

This paper cites an unresolved cited work.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Unresolved cited work

Reference 91

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:05:24.149904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f99986d6-19d0-4655-a60c-c3b6f1621d44 · outbound

This paper cites Note this matrix can be equivalently represented as H(x) = (p−2)∥u(x)∥ p−4∇u(x)⊤Gu(x)u(x)⊤G∇u(x).

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Note this matrix can be equivalently represented as H(x) = (p−2)∥u(x)∥ p−4∇u(x)⊤Gu(x)u(x)⊤G∇u(x)

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.138452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0f70308b-8ddf-43fd-8616-5d25a4da2f87 · outbound

This paper cites Then, we have the bound: ∥∇2f(x)−H(x)∥ ≤ ξ2 0 +ξ 1 f(x)≤ ξ2 0 +ξ 1 f⋆ +Dc∥∇f(x)∥ 1+c ∗ ,0≤c≤1.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Then, we have the bound: ∥∇2f(x)−H(x)∥ ≤ ξ2 0 +ξ 1 f(x)≤ ξ2 0 +ξ 1 f⋆ +Dc∥∇f(x)∥ 1+c ∗ ,0≤c≤1

Reference 93

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:05:24.127030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 944755e6-6fb2-43dd-886f-4d76539007c4 · outbound

This paper cites an unresolved cited work.

Gradient-Normalized Smoothness for Optimization with Approximate Hessians Unresolved cited work

Reference 94

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:05:24.113709Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

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