A stochastic inertial forward-backward splitting algorithm for\n multivariate monotone inclusions

2015/07/03 by Lorenzo Rosasco, Silvia Villa, Rosasco, Lorenzo +3 · 1 citation
Computer Science · Engineering · Mathematics · #47H05 #49M27 #49M29 #90C25 #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.1507.00848

openalex publication_date 2015/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an inertial forward-backward splitting algorithm to compute the\nzero of a sum of two monotone operators allowing for stochastic errors in the\ncomputation of the operators. More precisely, we establish almost sure\nconvergence in real Hilbert spaces of the sequence of iterates to an optimal\nsolution. Then, based on this analysis, we introduce two new classes of\nstochastic inertial primal-dual splitting methods for solving structured\nsystems of composite monotone inclusions and prove their convergence. Our\nresults extend to the stochastic and inertial setting various types of\nstructured monotone inclusion problems and corresponding algorithmic solutions.\nApplication to minimization problems is discussed.\n

Citations

• A Class of Randomized Primal-Dual Algorithms for Distributed Optimization

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