Publikation: On the forward–backward method with nonmonotone linesearch for infinite-dimensional nonsmooth nonconvex problems
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2025
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Computational Optimization and Applications. Springer. 2025, 91(3), S. 1263-1308. ISSN 0926-6003. eISSN 1573-2894. Verfügbar unter: doi: 10.1007/s10589-025-00684-x
Zusammenfassung
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.
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AZMI, Behzad, Marco BERNREUTHER, 2025. On the forward–backward method with nonmonotone linesearch for infinite-dimensional nonsmooth nonconvex problems. In: Computational Optimization and Applications. Springer. 2025, 91(3), S. 1263-1308. ISSN 0926-6003. eISSN 1573-2894. Verfügbar unter: doi: 10.1007/s10589-025-00684-xBibTex
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title={On the forward–backward method with nonmonotone linesearch for infinite-dimensional nonsmooth nonconvex problems},
year={2025},
doi={10.1007/s10589-025-00684-x},
number={3},
volume={91},
issn={0926-6003},
journal={Computational Optimization and Applications},
pages={1263--1308},
author={Azmi, Behzad and Bernreuther, Marco}
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