Sub‐gradient and Sub‐differential of Finite Convex Function
Mikhail Moklyachuk · 2021
For convex functions the notions of sub-gradient and sub-differential (set of sub-gradients) can be introduced. These generalizations of the concepts of gradient and differential are used in the theory of non-smooth convex optimization problems. This chapter deals with finite-valued convex functions. It describes the most common operations on convex functions that result in convex functions. The chapter shows how to calculate sub-differentials of these resulting convex functions. It also shows that the concepts of sub-gradient and sub-differential are closely related to the concept of a convex function. The chapter discusses some concepts from the theory of multivalued mappings. It formulates more general results for systems of linear inequalities and equations.