Second-order KKT optimality conditions for multi-objective optimal control problems

TL;DR

This paper establishes second-order KKT optimality conditions for multi-objective optimal control problems with constraints, providing a theoretical framework for analyzing local Pareto optimality without scalarization.

Contribution

It derives new second-order necessary and sufficient conditions for multi-objective optimal control problems satisfying Robinson's constraint qualification, avoiding scalarization methods.

Findings

Derived second-order optimality conditions for abstract problems

Applied conditions to specific multi-objective control problems

Provided direct, self-contained proofs without scalarization

Abstract

In this paper, we study second-order necessary and sufficient optimality conditions of Karush--Kuhn--Tucker-type for locally optimal solutions in the sense of Pareto to a class of multi-objective optimal control problems with mixed pointwise constraint. To deal with the problems, we first derive second-order optimality conditions for abstract multi-objective optimal control problems which satisfy the Robinson constraint qualification. We then apply the obtained results to our concrete problems. The proofs of obtained results are direct, self-contained without using scalarization techniques.