Proximal Algorithms for a class of abstract convex functions

Ewa Bednarczuk; Dirk Lorenz; The Hung Tran

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arXiv · 2402.17072

Proximal Algorithms for a class of abstract convex functions

Ewa Bednarczuk·Dirk Lorenz·The Hung Tran

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Abstract

In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of algorithms, namely an abstract proximal point method, an abstract forward-backward method and an abstract projected subgradient method. Global convergence results for all algorithms are discussed and numerical examples are given

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BibTeX RIS

Ewa Bednarczuk, Dirk Lorenz, The Hung Tran. 2024-02-26. Proximal Algorithms for a class of abstract convex functions. https://arxiv.org/abs/2402.17072

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