Yaohua Hu, Jingchao Li, Yanyan Liu, Carisa Kwok Wai Yu, Quasi-subgradient methods with Bregman distance for quasi-convex feasibility problems

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DOI: 10.23952/jnva.8.2024.3.03

Volume 8, Issue 3, 1 June 2024, Pages 381-395

Abstract. In this paper, we consider the quasi-convex feasibility problem (QFP), which is to find a common point of a family of sublevel sets of quasi-convex functions. By employing the Bregman projection mapping, we propose a unified framework of Bregman quasi-subgradient methods for solving the QFP. This paper is contributed to establish the convergence theory, including the global convergence, iteration complexity, and convergence rates, of the Bregman quasi-subgradient methods with several general control schemes, including the $\alpha$ -most violated constraints control and the s-intermittent control. Moreover, we introduce a notion of the Hölder-type bounded error bound property relative to the Bregman distance for the QFP, and use it to establish the linear (or sublinear) convergence rates for Bregman quasi-subgradient methods to a feasible solution of the QFP.

How to Cite this Article:
Y. Hu, J. Li, Y. Liu, C.K.W. Yu, Quasi-subgradient methods with Bregman distance for quasi-convex feasibility problems, J. Nonlinear Var. Anal. 8 (2024), 381-395.