Nonmonotone subgradient methods based on a local descent lemma

F. J. Aragón Artacho, R. Campoy García, P. Pérez Aros, D. Torregrosa Belén

In this talk, we extend the context of nonmonotone descent methods to a general class of nonsmooth and nonconvex functions satisfying a nonsmooth and local version of the descent lemma. Under this assumption, we propose a general subgradient method with a nonmonotone linesearch and prove subsequential convergence to stationary points. Our approach applies to a broad class of problems, including those involving forward–backward envelopes and augmented Lagrangians. We also report numerical results illustrating the advantages of the proposed method compared to existing algorithms.

Keywords: Optimization, Descent methods, nonsmooth

GT Optimización Continua II
September 2, 2026  3:30 PM
Aula 30

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