2013/08/04 by Nguyen Mau Nam, Nam, Nguyen Mau, Nguyễn Đình Hoàng +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1308.0775
openalex publication_date 2013/08/04 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28
In the early 1960's, Moreau and Rockafellar introduced a concept of called\n\subgradient for convex functions, initiating the developments of\ntheoretical and applied convex analysis. The needs of going beyond convexity\nmotivated the pioneer works by Clarke considering generalized differentiation\ntheory of Lipschitz continuous functions. Although Clarke generalized\ndifferentiation theory is applicable for nonconvex functions, convexity still\nplays a crucial role in Clarke subdifferential calculus. In the mid 1970's,\nMordukhovich developed another generalized differentiation theory for nonconvex\nfunctions and set-valued mappings in which the "umbilical cord with convexity"\nno longer exists. The primary goal of this paper is to present a unified\napproach and shed new light on convex and Clarke generalized differentiation\ntheories using the concepts and techniques from Mordukhovich's developments.\n