An Adaptive Partial Linearization Method for Optimization Problems on Product Sets

TL;DR

This paper introduces an adaptive partial linearization method for composite optimization on product sets, reducing computational costs while maintaining convergence, with demonstrated practical effectiveness.

Contribution

It presents a novel adaptive partial linearization algorithm tailored for composite optimization problems on product sets, improving efficiency and convergence analysis.

Findings

Reduces computational expenses per iteration.

Maintains convergence properties of the method.

Preliminary computational results show practical usefulness.

Abstract

We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the corresponding Cartesian product. The method consists in selective component-wise steps together with a special control of a tolerance sequence. This technique is destined to reduce the computational expenses per iteration and maintain the basic convergence properties. We also establish its convergence rates and describe some examples of applications. Preliminary results of computations illustrate usefulness of the new method.