Selective Bi-coordinate Method for Non-Stationary and Non-Smooth Resource Allocation Type Problems

TL;DR

This paper introduces a simple bi-coordinate variation method for non-stationary, non-smooth resource allocation problems with linear and box constraints, demonstrating convergence and computational advantages.

Contribution

It presents a novel bi-coordinate method tailored for non-stationary, non-smooth optimization, differing from traditional gradient-based approaches.

Findings

Method converges under mild assumptions.

Computational tests show advantages over existing methods.

Effective for problems with approximation sequences instead of exact data.

Abstract

We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the cost function and parameters of the feasible set. It consists in making descent steps with respect to only two selected coordinates satisfying some special threshold rule. The method is simpler essentially than the usual gradient or dual type ones and differs from the previous known bi-coordinate ones suggested for the usual stationary and smooth problems. We establish its convergence under rather mild assumptions. Computational tests also reveal certain preferences of the proposed method over the known ones.