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<p>This paper introduces and investigates a generalized prox-convexity notion for functions, aimed at designing algorithms to solve a class of nonconvex quasi-equilibrium problems, for which no previous methods were available. Based on this new concept, two Bregman proximal point-type algorithms are proposed, and their convergence is established under mild assumptions. Applications to generalized Nash-Cournot equilibrium and generalized Bertrand equilibrium models are presented.</p>

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Bregman Proximal Point Algorithms for Quasi-Equilibrium Problems Beyond Prox-Convexity

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • T. V. Thang

摘要

This paper introduces and investigates a generalized prox-convexity notion for functions, aimed at designing algorithms to solve a class of nonconvex quasi-equilibrium problems, for which no previous methods were available. Based on this new concept, two Bregman proximal point-type algorithms are proposed, and their convergence is established under mild assumptions. Applications to generalized Nash-Cournot equilibrium and generalized Bertrand equilibrium models are presented.