On some geometric conditions for minimality of DCH-functions via DC-duality approach

Abstract

In this study, some optimality conditions for DCH-functions are given in terms of -faces using DC-duality approach. We introduce some geometric characterizations for the solution set of DCH-minimization problems by means of exposed faces and Minkowski difference. Moreover, we prove that given conditions are independent of the choices of representatives of DCH-functions. Also, some of these conditions are employed to find inf-stationary points for a quasidifferentiable optimization problem (QDP), i.e., the directional derivative of the objective function is a DCH-function. Therefore, we present a condition to find stationary points of a QDP. We give some examples to illustrate obtained results.