Stochastic Proximal Point Methods for Monotone Inclusions under Expected Similarity

2024/05/23 by Abdurakhmon Sadiev, Laurent Condat, Sadiev, Abdurakhmon +3 · 4 citations
Business, Management and Accounting · Computer Science · Decision Sciences · #FOS: Mathematics #Facility Location and Emergency Management #Multi-Criteria Decision Making #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2405.14255

openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of possibly set-valued monotone operators, using at every iteration one call to the resolvent of a randomly sampled operator. We also introduce a notion of similarity between the operators, which holds even for discontinuous operators. We leverage it to derive linear convergence results in the strongly monotone setting.

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• The Stochastic Multi-Proximal Method for Nonsmooth Optimization

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