Constrained optimization through fixed point techniques

TL;DR

This paper presents a novel fixed point approach for solving constrained optimization problems, emphasizing simplicity, flexibility, and convergence, by treating multipliers as variables and seeking fixed points for a specific map.

Contribution

It introduces a new fixed point method for constrained optimization that differs from traditional dual strategies, enhancing simplicity and convergence.

Findings

Efficient computation of unconstrained solutions

Multipliers as variables in a fixed point map

Demonstrated convergence properties

Abstract

We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a certain map. Contrary to typical dual strategies, optimal vectors of multipliers are sought as fixed points for that map. Two distinctive features are worth highlighting: its simplicity and flexibility for the implementation, and its convergence properties.