New characterizations and preservation rules for variational convexity yield stronger local optimality guarantees in nonsmooth nonlinear programming problems.
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author Boyd, S
20 Pith papers cite this work, alongside 2,166 external citations. Polarity classification is still indexing.
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Uncorrected Gaussian residual penalties in full-space sampling converge after marginalization to the graph-lifted reduced posterior multiplied by the inverse absolute determinant of the state Jacobian, requiring explicit determinant corrections for equivalence.
Predictive coding equals proximal gradient descent on MAP problems, with priors setting nonlinearities via proximal operators and yielding leaky firing-rate networks plus hierarchical MRFs.
Neural networks can be parametrized to compute exact proximal operators that are provably equivariant to affine transformations, yielding better out-of-distribution performance on inverse problems.
A novel optimization algorithm reconstructs 3D refractive index in reflection-mode microscopy by exploiting multiply-scattered waves from uncontrolled background structures, using weighted time loss, positivity constraints, and total variation regularization, validated on simulations.
WaveDiff with wavefront feature projection recovers WFE from noisy undersampled in-focus observations at ~3% error, a tenfold improvement over the prior version.
ML-SPnP accelerates stochastic PnP for SVCT by using MRA approximation spaces where prior-coherence corrections vanish in expectation, yielding comparable quality at reduced runtime.
Presents a Moreau-Yosida regularized inversion framework in periodic Sobolev spaces to recover Kohn-Sham exchange-correlation potentials via proximal mapping and limiting procedure.
A Douglas-Rachford splitting algorithm with closed-form projection computes substantially sparser symmetric generalized inverses than the Moore-Penrose pseudoinverse for sparse symmetric matrices.
GAME is a convex estimator using overlapping nuclear-norm penalties on subgroup submatrices for low-rank matrix completion with known overlapping groups, providing finite-sample guarantees on reconstruction error and subgroup subspace recovery.
Kernelized convex clustering in RKHS with convergence guarantees, finite sample bounds, and empirical superiority on non-linear data.
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.
PDNS decomposes diffusion neural sampler training into proximal subproblems on path measures to gradually approach multimodal targets and promote mode exploration.
A high-dimensional Newey-Powell heteroscedasticity test is developed via expectile regression with limiting distribution and asymptotic power obtained through approximate message passing in the n/p to delta regime.
A prox-based semi-smooth Newton method is proposed for finite-element discretizations of convex variational problems, with global well-posedness and local superlinear convergence established under suitable assumptions on energy densities.
PatchCSI-T Transformer predicts multi-step CSI for adaptive underwater OFDM, improving BER and spectral efficiency on real UWA datasets.
Reinforcement learning learns a policy that adapts control parameters of a regularized interior-point method, accelerating high-accuracy solutions for convex quadratic programs and generalizing across problem classes after lightweight training.
A review of Faraday Rotation Measure Synthesis techniques and SKA Array Assembly stages for high-resolution Faraday tomography of cosmic magnetic structures.
Moreau-Yosida regularization supplies a convex-analysis tool that reformulates density-functional theory, defines Kohn-Sham systems rigorously, and connects to field theories through topology.
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Variational convexity: new characterizations, calculus rules, and applications
New characterizations and preservation rules for variational convexity yield stronger local optimality guarantees in nonsmooth nonlinear programming problems.
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Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems
Uncorrected Gaussian residual penalties in full-space sampling converge after marginalization to the graph-lifted reduced posterior multiplied by the inverse absolute determinant of the state Jacobian, requiring explicit determinant corrections for equivalence.
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Predictive Coding with Bayesian Priors via Proximal Gradients
Predictive coding equals proximal gradient descent on MAP problems, with priors setting nonlinearities via proximal operators and yielding leaky firing-rate networks plus hierarchical MRFs.
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Learning Affine-Equivariant Proximal Operators
Neural networks can be parametrized to compute exact proximal operators that are provably equivariant to affine transformations, yielding better out-of-distribution performance on inverse problems.
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Taking advantage of multiple scattering for Optical Reflection Tomography
A novel optimization algorithm reconstructs 3D refractive index in reflection-mode microscopy by exploiting multiply-scattered waves from uncontrolled background structures, using weighted time loss, positivity constraints, and total variation regularization, validated on simulations.
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WaveDiff with wavefront feature projection recovers WFE from noisy undersampled in-focus observations at ~3% error, a tenfold improvement over the prior version.
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Multilevel Stochastic Plug-and-Play for Sparse-View CT Reconstruction
ML-SPnP accelerates stochastic PnP for SVCT by using MRA approximation spaces where prior-coherence corrections vanish in expectation, yielding comparable quality at reduced runtime.
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Moreau-Yosida-based Kohn-Sham Inversion for Periodic Systems
Presents a Moreau-Yosida regularized inversion framework in periodic Sobolev spaces to recover Kohn-Sham exchange-correlation potentials via proximal mapping and limiting procedure.
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Sparse symmetric generalized inverses for sparse symmetric matrices
A Douglas-Rachford splitting algorithm with closed-form projection computes substantially sparser symmetric generalized inverses than the Moore-Penrose pseudoinverse for sparse symmetric matrices.
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Group-Aware Matrix Estimation and Latent Subspace Recovery
GAME is a convex estimator using overlapping nuclear-norm penalties on subgroup submatrices for low-rank matrix completion with known overlapping groups, providing finite-sample guarantees on reconstruction error and subgroup subspace recovery.
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A New Framework for Convex Clustering in Kernel Spaces: Finite Sample Bounds, Consistency and Performance Insights
Kernelized convex clustering in RKHS with convergence guarantees, finite sample bounds, and empirical superiority on non-linear data.
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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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Proximal Diffusion Neural Sampler
PDNS decomposes diffusion neural sampler training into proximal subproblems on path measures to gradually approach multimodal targets and promote mode exploration.
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High-dimensional Newey-Powell Test Via Approximate Message Passing
A high-dimensional Newey-Powell heteroscedasticity test is developed via expectile regression with limiting distribution and asymptotic power obtained through approximate message passing in the n/p to delta regime.
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A $\operatorname{prox}$-Based Semi-Smooth Newton Method for Convex Variational Problems
A prox-based semi-smooth Newton method is proposed for finite-element discretizations of convex variational problems, with global well-posedness and local superlinear convergence established under suitable assumptions on energy densities.
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Deep Learning Based Multi-Step Channel Prediction for Adaptive Underwater Acoustic OFDM Systems
PatchCSI-T Transformer predicts multi-step CSI for adaptive underwater OFDM, improving BER and spectral efficiency on real UWA datasets.
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Reinforcement learning for adaptive interior point methods in convex quadratic programming
Reinforcement learning learns a policy that adapts control parameters of a regularized interior-point method, accelerating high-accuracy solutions for convex quadratic programs and generalizing across problem classes after lightweight training.
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Faraday Tomography with the SKA: A New Era of Cosmic Magnetism Studies
A review of Faraday Rotation Measure Synthesis techniques and SKA Array Assembly stages for high-resolution Faraday tomography of cosmic magnetic structures.
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Perspective on Moreau-Yosida Regularization in Density-Functional Theory
Moreau-Yosida regularization supplies a convex-analysis tool that reformulates density-functional theory, defines Kohn-Sham systems rigorously, and connects to field theories through topology.
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