Local stability of solutions to a parametric multi-objective optimal control problem

Abstract

This paper studies local stability of solutions to a parametric multi-objective optimal control problem with constraints. By combining the scalarization method and non-scalarization methods, we show that if the unperturbed problem has a locally strong Pareto solution, then the Pareto solution set is locally Hölder continuous at a reference parameter.

Keywords:

• Stability of solutions
• parametric multi-objective optimal control problem
• Pareto solution
• Hölder continuity
• Lipschitz continuity

AMS Subject Classifications:

• 49K20
• 35J25

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Vietnam Academy of Science and Technology under Grant Number CTTH00.01/22-23.