Variations of the infimal convolution and application to the minimal time function.

Abstract:

We establish in the Banach setting a relationship between the variations of the infimal convolution of a fairly general function and a proper continuous convex function. Namely, we compare the Clarke subdifferential of all these functions at points where the infimal convolution is attained, or strongly attained. This work extends and adapts many of the existing results in the literature. We apply this work to investigate the differentiability of a minimal time function. We also discuss necessary optimality conditions for a location problem.

Posted on Aug 24, 2016 in Optimization and Equilibrium, Seminars