QUASI-SUBGRADIENT METHODS WITH BREGMAN DISTANCE FOR QUASI-CONVEX FEASIBILITY PROBLEMS

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 Hodlder-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.