Some characterizations of a nonlinear scalarizing function via oriented distance function

Abstract

This paper aims at investigating some properties concerned with a nonlinear scalarizing function via oriented distance function. The convexity, continuity and Lipschitz continuity of the nonlinear scalarizing function are showed under some suitable conditions. As an application, we establish Lipschitz continuity of strongly approximate solution mapping for l-type order relation to parametric set optimization problems by using convexity and Lipschitz continuity of the nonlinear scalarizing function.