Splitting proximal with penalization schemes for additive convex hierarchical minimization problems

Abstract

ABSTRACT 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 convex hierarchical minimization problem. Some numerical experiments on the regularized least squares problems are given to show the effectiveness of the obtained theoretical results.