Tangential Extremal Principles for Finite and Infinite Systems of Sets, I: Basic Theory

TL;DR

This paper introduces tangential extremal principles in variational analysis for finite and infinite systems of convex and nonconvex sets, unifying primal and dual methods and applying to semi-infinite programming and multiobjective optimization.

Contribution

It develops new extremal principles that unify primal and dual approaches for systems of sets, extending to infinite systems and applications.

Findings

Established foundational tangential extremal principles.

Unified primal-dual approach for variational systems.

Applied principles to semi-infinite programming and multiobjective optimization.

Abstract

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. The first part of the paper concerns the basic theory of tangential extremal principles while the second part presents applications to problems of semi-infinite programming and multiobjective optimization.