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Proximal Method with Penalization for Split Hierarchical Minimization Problems

Nimit Nimana(nimitn***at***hotmail.com)
Narin Petrot(narinp***at***nu.ac.th)

Abstract: In this paper we consider a splitting proximal algorithm with penalization for minimizing a finite sum of proper, convex and lower semicontinuous functions subject to the set of minimizers of another proper, convex and lower semicontinuous function. We show convergences of the generated sequence of iterates to an optimal solution of the considered hierarchical minimization problem. As an illustrative example, some numerical experiments on the regularized least squares problems are given to show the effectiveness of the obtained theoretical results.

Keywords: Split hierarchical minimization; convex optimization; penalization; proximal algorithm; regularized least squares problems

Category 1: Convex and Nonsmooth Optimization


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Entry Submitted: 06/09/2017
Entry Accepted: 06/09/2017
Entry Last Modified: 06/09/2017

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