Almost-Surely Convergent Randomly Activated Monotone Operator Splitting Methods

2024/03/15 by Patrick L. Combettes, Combettes, Patrick L., Javier I. Madariaga +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2403.10673

openalex publication_date 2024/03/15 · openalex created_date 2024/03/20 · openalex updated_date 2026/07/28

Abstract

We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and, unlike existing methods, achieve almost sure convergence of the iterates to a solution without any regularity assumptions or knowledge of the norms of the linear operators. Applications to image recovery and machine learning are provided.

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