Explicit counterexamples in Hilbert spaces show Cesàro means of firmly nonexpansive iterates need not converge strongly.
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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.
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.
A variable-metric non-monotone line search method based on the Fukushima regularized gap function is introduced for mixed variational inequalities and equilibrium problems, with global convergence and R-linear rate proved under strong monotonicity.
Presents a Moreau-Yosida regularized inversion framework in periodic Sobolev spaces to recover Kohn-Sham exchange-correlation potentials via proximal mapping and limiting procedure.
CRM initialized in V converges linearly at the sharp rate ρ_V = (sin²θ_p - sin²θ_F)/(sin²θ_p + sin²θ_F) which is optimal for parameter-free single-step methods and smaller than c_F².
FRAMES uses Moreau envelope smoothing with Frank-Wolfe steps for nonsmooth nonconvex problems, proving convergence rates under mild assumptions and highlighting a new gap relationship.
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.
Develops multiplier-based contraction framework and LMI conditions for stability of regularized MPC interpreted as implicit Lur'e systems across three classes of regularizers.
Derives criteria for when state-dependent proto-area two-jets in approximate holographic codes are compatible with metric two-jets, including polyhedral realizations, X-ray transform tangent spaces, and quadratic obstructions to geometry.
Proves time-averaged reconstruction errors converge to zero in online dynamic inverse problems as noise, algorithmic errors, and regularization vanish with growing horizon.
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.
citing papers explorer
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Ces\`aro means of firmly nonexpansive iterates need not converge strongly
Explicit counterexamples in Hilbert spaces show Cesàro means of firmly nonexpansive iterates need not converge strongly.
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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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A Variable-Metric Non-monotone Line Search Method for Mixed Variational Inequalities and Equilibrium Problems
A variable-metric non-monotone line search method based on the Fukushima regularized gap function is introduced for mixed variational inequalities and equilibrium problems, with global convergence and R-linear rate proved under strong monotonicity.
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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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On the sharp linear convergence rate of the circumcentered--reflection method on subspaces
CRM initialized in V converges linearly at the sharp rate ρ_V = (sin²θ_p - sin²θ_F)/(sin²θ_p + sin²θ_F) which is optimal for parameter-free single-step methods and smaller than c_F².
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Frank-Wolfe with Moreau Envelope Smoothing for Nonsmooth Nonconvex Problems
FRAMES uses Moreau envelope smoothing with Frank-Wolfe steps for nonsmooth nonconvex problems, proving convergence rates under mild assumptions and highlighting a new gap relationship.
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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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Regularized Model Predictive Control via Contractivity and Implicit Lur'e Analysis
Develops multiplier-based contraction framework and LMI conditions for stability of regularized MPC interpreted as implicit Lur'e systems across three classes of regularizers.
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Nonlinear Geometrizability of State-Dependent Proto-Area in Approximate Holographic Codes
Derives criteria for when state-dependent proto-area two-jets in approximate holographic codes are compatible with metric two-jets, including polyhedral realizations, X-ray transform tangent spaces, and quadratic obstructions to geometry.
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Dynamic inverse problems: Online regularisation theory
Proves time-averaged reconstruction errors converge to zero in online dynamic inverse problems as noise, algorithmic errors, and regularization vanish with growing horizon.
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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.