Geometric approach to convex subdifferential calculus. (3rd June 2017)

• Record Type: Journal Article
• Authors: Mordukhovich, Boris S.; Nam, Nguyen Mau
• Is Part Of: Optimization. Volume 66:Number 6(2017)
• Page Start: 839
• Page End: 873
• Publication Date: 2017-06-03
• Subjects: convex analysis -- generalized differentiation -- geometric approach -- convex separation -- normal cone -- subdifferential -- coderivative -- calculus rules -- maximum function -- optimal value function; 49J52 -- 49J53 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1105225
• Languages: English
• ISSNs: 0233-1934

Abstract

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 optimal value/marginal functions, normals to 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 parameterized generalized equations governed by set-valued mappings with convex graphs.