Incremental proximal gradient scheme with penalization for constrained\n composite convex optimization problems

2019/09/11 by Nimit Nimana, Nimana, Nimit, Narin Petrot +1
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1909.05060

openalex publication_date 2019/09/11 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We consider the problem of minimizing a finite sum of convex functions\nsubject to the set of minimizers of a convex differentiable function. In order\nto solve the problem, an algorithm combining the incremental proximal gradient\nmethod with smooth penalization technique is proposed. We show the convergence\nof the generated sequence of iterates to an optimal solution of the\noptimization problems, provided that a condition expressed via the Fenchel\nconjugate of the constraint function is fulfilled. Finally, the functionality\nof the method is illustrated by some numerical experiments addressing image\ninpainting problems and generalized Heron problems with least squares\nconstraints.\n

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