Work

On the forward–backward method with nonmonotone linesearch for infinite-dimensional nonsmooth nonconvex problems

Year: 2025

Type: article

Abstract: This paper provides a comprehensive study of the nonmonotone forward–backward splitting (FBS) method for solving a class of nonsmooth composite problems in Hilbert spaces. The objective function is the sum of a Fréchet differentiable (not necessarily convex) function and a proper lower semicontinuous convex (not necessarily smooth) function. These problems appear, for example, frequently in the context of optimal control of nonlinear partial differential equations (PDEs) with nonsmooth sparsity-promoting cost functionals. We discuss the convergence and complexity of FBS equipped with the nonmonotone linesearch under different conditions. In particular, R-linear convergence will be derived under quadratic growth-type conditions. We also investigate the applicability of the algorithm to problems governed by PDEs. Numerical experiments are also given that justify our theoretical findings.

Source: Computational Optimization and Applications

DOI: 10.1007/s10589-025-00684-x

Authors: Behzad Azmi, Marco Bernreuther

Institutions: University of Konstanz, University of Stuttgart

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Deutsche Forschungsgemeinschaft, Universität Konstanz