Necessary and sufficient conditions for local Pareto optimality on time scales

TL;DR

This paper establishes necessary and sufficient conditions for local Pareto optimality in multiobjective variational problems on time scales, extending optimality theory to a unified dynamic framework.

Contribution

It provides the first comprehensive set of conditions for weak local Pareto optimality and necessary conditions for isoperimetric problems with multiple constraints on time scales.

Findings

Necessary and sufficient conditions for weak local Pareto optimality.

Necessary optimality condition for multi-constraint isoperimetric problems.

Extension of variational optimality conditions to the time scales setting.

Abstract

We study a multiobjective variational problem on time scales. For this problem, necessary and sufficient conditions for weak local Pareto optimality are given. We also prove a necessary optimality condition for the isoperimetric problem with multiple constraints on time scales.