The effect of deterministic noise on a quasi-subgradient method for quasi-convex feasibility problems

Abstract

. The quasi-convex feasibility problem (QFP), in which the involved functions are quasi-convex, is at the core of the modeling of many problems in various areas such as economics, finance and management science. In this paper, we consider an inexact incremental quasi-subgradient method to solve the QFP, in which an incremental control of component functions in the QFP is employed and the inex-actness stems from computation error and noise arising from practical considerations and physical cir-cumstances. Under the assumptions that the computation error and noise are deterministic and bounded and a H¨older condition on component functions in the QFP, we study the convergence property of the proposed inexact incremental quasi-subgradient method, and particularly, investigate the effect of the inexact terms on the incremental quasi-subgradient method when using the constant, diminishing and dynamic stepsize rules.