No-gap optimality conditions for an optimal control problem with pointwise control-state constraints. Issue 6 (26th April 2019)

• Record Type: Journal Article
• Authors: Son, Nguyen Hai; Nguyet, Tran Minh
• Is Part Of: Applicable analysis. Volume 98:Issue 6(2019)
• Page Start: 1120
• Page End: 1142
• Publication Date: 2019-04-26
• Subjects: Navier–Stokes–Voigt equations -- second-order necessary optimality conditions -- second-order sufficient optimality conditions -- optimal control -- no-gap conditions; 49K20 -- 35J25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1416102
• Languages: English
• ISSNs: 0003-6811

Abstract

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.