Rated Extremal Principles for Finite and Infinite Systems

TL;DR

This paper introduces rated extremal principles for finite and infinite systems of closed sets, advancing the geometric theory of variational analysis and enabling new calculus and optimality conditions for problems with infinitely many constraints.

Contribution

It develops new notions of local extremality called rated extremal principles and applies them to variational analysis and constrained optimization.

Findings

Established rated extremal principles for finite and infinite systems.

Applied principles to derive calculus and optimality conditions.

Enhanced understanding of extremality in variational analysis.

Abstract

In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the core geometric theory of variational analysis. We present their applications to calculus and optimality conditions for problems with infinitely many constraints.