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

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Proximal Algorithms for a Class of Abstract Convex Functions

  • 期刊论文

  • 发表日期：

    2025年2月4日

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  • Ewa Bednarczuk,
  • Dirk Lorenz,
  • The Hung Tran

摘要

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