A primal-dual splitting algorithm for finding zeros of sums of maximally\n monotone operators

2012/06/26 by Radu Ioan Boţ, Bot, Radu Ioan, Ernö Robert Csetnek +3 · 1 citation
Computer Science · Engineering · Mathematics · #47H05 #65K05 #90C25 #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1206.5953

openalex publication_date 2012/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the primal problem of finding the zeros of the sum of a maximally\nmonotone operator with the composition of another maximally monotone operator\nwith a linear continuous operator and a corresponding dual problem formulated\nby means of the inverse operators. A primal-dual splitting algorithm which\nsimultaneously solves the two problems in finite-dimensional spaces is\npresented. The scheme uses at each iteration separately the resolvents of the\nmaximally monotone operators involved and it gives rise to a splitting\nalgorithm for finding the zeros of the sum of compositions of maximally\nmonotone operators with linear continuous operators. The iterative schemes are\nused for solving nondifferentiable convex optimization problems arising in\nimage processing and in location theory.\n

Cited by

• A Douglas-Rachford type primal-dual method for solving inclusions with\n mixtures of composite and parallel-sum type monotone operators

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