Properties of uniform tangent sets and Lagrange multiplier rule

TL;DR

This paper investigates uniform tangent sets and extends the abstract Lagrange multiplier rule, providing deeper theoretical insights into their properties and generalizations within control optimization contexts.

Contribution

It advances the theory of uniform tangent sets and generalizes the Lagrange multiplier rule, building on prior foundational work.

Findings

Enhanced understanding of uniform tangent sets

Generalized Lagrange multiplier rule

Theoretical framework for control optimization

Abstract

The concept of uniform tangent sets was introduced and discussed in [3 - Krastanov, Ribarska, SIAM J. Control Optim., 55(3), 2017]. This study is devoted to their further investigation and to generalization of the abstract Lagrange multiplier rule from [3].