No-gap optimality conditions for an optimal control problem with pointwise control-state constraints

ABSTRACT

An optimal control problem with pointwise mixed constraints of the instationary three-dimensional Navier–Stokes–Voigt equations is considered. We derive second-order optimality conditions and show that there is no gap between second-order necessary optimality conditions and second-order sufficient optimality conditions. In addition, the second-order sufficient optimality conditions for the problem where the objective functional does not contain a Tikhonov regularization term are also discussed.

KEYWORDS:

• Navier–Stokes–Voigt equations
• second-order necessary optimality conditions
• second-order sufficient optimality conditions
• optimal control
• no-gap conditions

AMS SUBJECT CLASSIFICATIONS:

• 49K20
• 35J25

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.01-2015.13].