An Inexact First-order Method for Constrained Nonlinear Optimization

TL;DR

This paper introduces an inexact first-order method for constrained nonlinear optimization that reduces computational costs, detects infeasibility automatically, and guarantees global convergence with proven complexity bounds.

Contribution

It presents a novel inexact first-order algorithm with a penalty parameter strategy, enabling efficient solving of constrained nonlinear problems with convergence guarantees.

Findings

Algorithm efficiently finds inexact solutions

Reduces computational cost per iteration

Proven global convergence and complexity bounds

Abstract

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the computational cost needed for each iteration. A penalty parameter updating strategy during the process of solving the subproblem enables the algorithm to automatically detect infeasibility. Global convergence for both feasible and infeasible cases are proved. Complexity analysis for the KKT residual is also derived under mild assumptions. Numerical experiments exhibit the ability of the proposed algorithm to rapidly find inexact optimal solution through cheap computational cost.