New extremal principles with applications to stochastic and semi-infinite programming

TL;DR

This paper introduces new extremal principles in variational analysis tailored for stochastic and semi-infinite programming, enabling advanced normal cone estimates without relying on smoothness or convexity.

Contribution

It develops novel extremal principles for measurable set-valued mappings, facilitating variational analysis in non-smooth, non-convex stochastic and semi-infinite optimization problems.

Findings

Derived integral representations of normal cones.

Established upper estimates for normal cones to set intersections.

Applied principles to stochastic and semi-infinite programming contexts.

Abstract

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of sets defined by measurable multifunctions, which are in turn crucial for novel applications to stochastic and semi-infinite programming.