High order tangent vectors to sets with applications to constrained optimization problems

TL;DR

This paper introduces a high-order tangent cone concept to better approximate sets and applies it to derive advanced necessary conditions for optimality in constrained optimization problems.

Contribution

It presents a novel high-order tangent cone framework and demonstrates its use in formulating more precise optimality conditions.

Findings

Defined an extended high-order tangent cone.

Derived high-order necessary optimality conditions.

Enhanced understanding of local minimizers in constrained problems.

Abstract

We introduce an extended tangent cone of high order to a set and study its properties. Then we use this local approximation for deriving high-order necessary conditions for local minimizers of constrained optimization problems.