A global and superlinearly convergent algorithm for nonlinear nondifferential convex programming problems with a generalized Armijo line-search

TL;DR

This paper introduces a new generalized Armijo line-search algorithm for solving broad classes of nonlinear, non-smooth convex programming problems, achieving global and superlinear convergence under weak conditions.

Contribution

It develops a novel line-search method combined with phi-regulation, extending previous results to more general non-smooth convex optimization problems with proven convergence properties.

Findings

Proved global convergence of the algorithm.

Established superlinear convergence rate.

Extended previous results to broader problem classes.

Abstract

This paper presents a new generalized Armijo's line-search method, and combines it with a phi-regulation defined to obtain a new algorithm solving the very general non-linear non-smooth convex programming. For the algorithm designed, the global convergence is proved and the algorithm has super-linear convergent rate under very weak conditions. This paper generalized the results of reference "Fukushima M and Qi LQ (1996) SIAM Journal of Optimization 6: 1106-20".