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

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 inexactness stems from computation error and noise arising from practical considerations and physical circumstances. Under the assumptions that the computation error and noise are deterministic and bounded and a Hölder 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. © 2020 Journal of Applied and Numerical Optimization.