Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.10.2026.3.09

Volume 10, Issue 3, 1 June 2026, Pages 687-701

 

Abstract. The feasibility problem lies at the core of modeling numerous challenges across mathematics and the physical sciences. Quasi-convex functions, widely applied in economics, finance, and management science, offer a flexible framework for such problems. This paper addresses the stochastic quasi-convex feasibility problem (SQFP), which seeks a common point within infinitely many sublevel sets of quasi-convex functions. Inspired by the idea of a stochastic index scheme and Bregman projection, we propose a stochastic quasi-subgradient method with Bregman projection to solve the SQFP, in which the quasi-subgradients of a random (and finite) index set of component quasi-convex functions at the current iterate are used to construct the descent direction and employ the Bregman projection in place of the Euclidean projection at each iteration. Furthermore, we introduce a notion of Hölder-type bounded error bound property relative to the Bregman projection and random control sequence for the SQFP. Leveraging this property, we establish a global convergence theorem and quantify convergence rates for the proposed algorithm. This paper reveals that the stochastic quasi-subgradient method with Bregman projection offers both low computational cost requirement and fast convergence feature.

 

How to Cite this Article:
Y. Hu, J. Li, C. Yang, C.K.W. Yu, Stochastic quasi-subgradient methods with Bregman projection for stochastic quasi-convex feasibility problems, J. Nonlinear Var. Anal. 10 (2026), 687-701.