A subgradient method with non-monotone line search

O P Ferreira (1) , G N Grapiglia (2) , E M Santos (3) , J C O Souza (4, 5)

1 UFG - Universidade Federal de Goiás [Goiânia]
2 UCL - Université Catholique de Louvain = Catholic University of Louvain
3 IFCE - Instituto Federal de Educação, Ciência e Tecnologia do Maranhão
4 Federal University of Piauí
5 AMSE - Aix-Marseille Sciences Economiques

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.

Keywords: Subgradient method; Non-monotone line search; Convex function

Domains: Mathematics [math]; Humanities and Social Sciences; Economics and Finance

O P Ferreira, G N Grapiglia, E M Santos, J C O Souza. A subgradient method with non-monotone line search. Computational Optimization and Applications, In press, ⟨10.1007/s10589-022-00438-z⟩. ⟨hal-03880925⟩