Prox-ITEM achieves the minimax-optimal distance-to-solution rate among span-based first-order methods for smooth strongly convex composite problems, with Prox-TMM as its stationary limit matching TMM rates.
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13 Pith papers cite this work. Polarity classification is still indexing.
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SiMPL generates feasible iterates for multi-material topology optimization by using tailored Bregman divergences to enforce point-wise polytopal design constraints, with global constraints handled via a small dual problem.
A communication-efficient distributed algorithm is proposed for fixed-point seeking of biased stochastic operators using inexact iterations, compression, and period skipping, with convergence shown under relaxed conditions and unified with non-convex optimization.
QOP achieves (ε, δ)-differential privacy for ERM in the interpolation regime under weaker assumptions than linear objective perturbation by using random quadratic curvature to enforce stability and control sensitivity.
A subgradient method for convex inequality systems in Hilbert space has finite termination when the system is strictly feasible and subgradients are bounded.
Nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity, applied to quasi-optimal finite-element error estimates for viscous Hamilton-Jacobi equations and second-order mean field games.
Fully implicit resolvent discretization of noisy accelerated gradient dynamics produces a Lyapunov mean-square recursion whose contraction factor improves and stationary error scales as O(1/α), vanishing for large α under accurate inner solves.
Chambolle-Pock converges weakly to a KKT point for 0 < θ ≤ 1 when τσ‖L‖² is below 4θ(2-θ)/(1-2θ+9θ²-4θ³), with ergodic duality gap O(1/k).
Develops a dissipativity and contraction theory framework for convergence analysis of distributed optimization algorithms, producing LMI conditions for arbitrary network structures.
Binno is a proximal-gradient first-order algorithm for nonconvex nonsmooth bi-level optimization, shown on sparse low-rank matrix factorization and regularized market-clearing problems with reported gains over baselines.
New inconsistent alternating projection scheme for basis pursuit with linear convergence proofs and competitive benchmarks.
Adaptive λ adjustment for target sparsity in LinBreg and AdaBreg, shown to work on speaker verification models with ECAPA-TDNN and ResNet34.
Investigates Fejér* monotonicity in Hilbert spaces for optimization algorithms, its weak and strong convergence, and comparisons to quasi-Fejér-type notions via examples.
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An optimal first-order method for smooth and strongly convex composite optimization and its stationary limit
Prox-ITEM achieves the minimax-optimal distance-to-solution rate among span-based first-order methods for smooth strongly convex composite problems, with Prox-TMM as its stationary limit matching TMM rates.
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The SiMPL Method for Multi-Material Topology Optimization
SiMPL generates feasible iterates for multi-material topology optimization by using tailored Bregman divergences to enforce point-wise polytopal design constraints, with global constraints handled via a small dual problem.
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Distributed Seeking for Fixed Points of Biased Stochastic Operators: A Communication-Efficient Approach
A communication-efficient distributed algorithm is proposed for fixed-point seeking of biased stochastic operators using inexact iterations, compression, and period skipping, with convergence shown under relaxed conditions and unified with non-convex optimization.
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Quadratic Objective Perturbation: Curvature-Based Differential Privacy
QOP achieves (ε, δ)-differential privacy for ERM in the interpolation regime under weaker assumptions than linear objective perturbation by using random quadratic curvature to enforce stability and control sensitivity.
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Finite Termination of a Generalized Perceptron Algorithm
A subgradient method for convex inequality systems in Hilbert space has finite termination when the system is strictly feasible and subgradients are bounded.
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A nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity techniques and applications to nonlinear PDEs
Nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity, applied to quasi-optimal finite-element error estimates for viscous Hamilton-Jacobi equations and second-order mean field games.
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IRON: Implicit Resolvent Optimization under Noise
Fully implicit resolvent discretization of noisy accelerated gradient dynamics produces a Lyapunov mean-square recursion whose contraction factor improves and stationary error scales as O(1/α), vanishing for large α under accurate inner solves.
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The Chambolle-Pock method also converges weakly with $0 < \theta \le 1$ and $\tau\sigma\|L\|^{2} < 4\theta(2-\theta)/(1 - 2\theta + 9\theta^{2} - 4\theta^{3})$
Chambolle-Pock converges weakly to a KKT point for 0 < θ ≤ 1 when τσ‖L‖² is below 4θ(2-θ)/(1-2θ+9θ²-4θ³), with ergodic duality gap O(1/k).
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Convergence Analysis of Distributed Optimization: A Dissipativity Framework
Develops a dissipativity and contraction theory framework for convergence analysis of distributed optimization algorithms, producing LMI conditions for arbitrary network structures.
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Binno: A 1st-order method for Bi-level Nonconvex Nonsmooth Optimization for Matrix Factorizations
Binno is a proximal-gradient first-order algorithm for nonconvex nonsmooth bi-level optimization, shown on sparse low-rank matrix factorization and regularized market-clearing problems with reported gains over baselines.
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Basis pursuit by inconsistent alternating projections
New inconsistent alternating projection scheme for basis pursuit with linear convergence proofs and competitive benchmarks.
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Adaptive Regularization for Sparsity Control in Bregman-Based Optimizers
Adaptive λ adjustment for target sparsity in LinBreg and AdaBreg, shown to work on speaker verification models with ECAPA-TDNN and ResNet34.
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Fej\'er* monotonicity in optimization algorithms
Investigates Fejér* monotonicity in Hilbert spaces for optimization algorithms, its weak and strong convergence, and comparisons to quasi-Fejér-type notions via examples.