The convexity principle for set-valued mappings and application to local programming
Van Ngai Huynh, Han Dao Ngoc · Pacific Journal of Optimization · 2024
(Communicated by Xinmin Yang) Abstract: In the papers ([1, 2]), Polyak has established a convexity principle, stated that the image of a small ball by a C1,1−smooth mapping between Hilbert spaces is convex. This convexity principle has some interesting applications in optimization and control theory. In this note, we give an extension of this principle to weakly convex multifunctions and its applications to local programming.