Nonmonotone subgradient methods based on a local descent lemma
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