Geometric Approach to Subdifferential Calculus

TL;DR

This paper introduces a geometric method for convex subdifferential calculus in finite dimensions, simplifying proofs and deriving new results in convex analysis using variational analysis concepts.

Contribution

It presents a novel geometric approach that simplifies proofs and extends convex subdifferential calculus with new results on marginal functions, normal cones, and coderivatives.

Findings

Simplified proofs of basic convex subdifferential calculus results

New results on marginal and normal functions in convex analysis

Calculations of coderivatives for solution maps in convex generalized equations

Abstract

In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic results of convex subdifferential calculus in full generality and also derive new results of convex analysis concerning marginal/value functions, normal of inverse images of sets under set-valued mappings, calculus rules for coderivatives of single-valued and set-valued mappings, and calculating coderivatives of solution maps to convex generalized equations.