Introduces APS, an adaptive proximal method achieving O(ε^{-2}) iteration complexity for ε-stationary points of ρ-weakly convex functions with unknown ρ in deterministic and stochastic settings.
The proximal point method revisited
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this short survey, I revisit the role of the proximal point method in large scale optimization. I focus on three recent examples: a proximally guided subgradient method for weakly convex stochastic approximation, the prox-linear algorithm for minimizing compositions of convex functions and smooth maps, and Catalyst generic acceleration for regularized Empirical Risk Minimization.
fields
math.OC 4years
2026 4representative citing papers
A diameter criterion tied to a potential function certifies convergence of difference inclusions, enabling discrete proofs for first-order optimization methods with diminishing steps.
Restart schemes for SGD on KL-satisfying non-smooth weakly convex problems deliver accelerated convergence robust to exponent misspecification, with optimal schedules resembling Polyak steps.
Robust learning problems are formulated as quasar-convex optimization, and HiPPA is proposed as an inexact high-order proximal method with global and superlinear convergence guarantees.
citing papers explorer
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Restart and Adaptive Acceleration in Stochastic Gradient Methods
Restart schemes for SGD on KL-satisfying non-smooth weakly convex problems deliver accelerated convergence robust to exponent misspecification, with optimal schedules resembling Polyak steps.