Paper dedicated to Jon Borwein

by Boris S. Mordukhovich and N. M. Nam
Dedicated to the memory of Jonathan Michael Borwein

Abstract: In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new calculus results on intersection rules for normal cones to convex sets and on infimal convolutions of support functions.

From Introduction: Convex analysis has been well recognized as an important area of mathematics with numerous applications to optimization, control, economics, and many other disciplines. Jon Borwein, who unexpectedly passed away on August 2, 2016, made pivotal contributions to these and related fields of Applied Mathematics, among other areas of his fantastic creative activity.

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