A subgradient method with non-monotone line search

TL;DR

This paper introduces an adaptive subgradient method with non-monotone line search for convex optimization, providing convergence guarantees and demonstrating improved efficiency over traditional fixed-step approaches.

Contribution

It proposes a novel subgradient algorithm with adaptive step sizes and non-monotone line search, enhancing convergence and efficiency in convex constrained problems.

Findings

Convergence is achieved under mild conditions.

The method shows superior efficiency in preliminary tests.

Provides iteration-complexity bounds for the algorithm.

Abstract

In this paper we present a subgradient method with non-monotone line search for the minimization of convex functions with simple convex constraints. Different from the standard subgradient method with prefixed step sizes, the new method selects the step sizes in an adaptive way. Under mild conditions asymptotic convergence results and iteration-complexity bounds are obtained. Preliminary numerical results illustrate the relative efficiency of the proposed method.