Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations

被引：4

作者：

Bui Trong Kien ^{[1
]}

机构：

[1] Vietnam Acad Sci & Technol, Inst Math, Dept Optimizat & Control Theory, 18 Hoang Quoc Viet Rd, Hanoi, Vietnam

来源：

ACTA MATHEMATICA VIETNAMICA | 2019年 / 44卷 / 02期

关键词：

Optimal control; Stationary Navier-stokes equations; Solution stability; Locally upper Holder continuity; Second-order necessary optimality condition; Second-order sufficient optimality condition;

D O I：

10.1007/s40306-018-00304-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a class of parametric optimal control problems governed by stationary Navier-Stokes equations with mixed pointwise constraints is considered. We give no-gap second-order necessary and sufficient conditions for unperturbed problem. We show that if the strictly second-order sufficient condition for unperturbed problem is valid and the objective function is locally Lipschitz continuous, then the solution map is locally upper Holder continuous at the reference parameter.

引用

页码：431 / 448

页数：18

共 50 条

[11] A projection-based variational multiscale method for the optimal control problems governed by the stationary Navier-Stokes equations
Yilmaz, Fikriye
Cibik, Aytekin
APPLIED NUMERICAL MATHEMATICS, 2016, 106 : 116 - 128
[12] Existence of an optimal solution of a shape control problem for the stationary Navier-Stokes equations
Iowa State Univ, Ames, United States
SIAM J Control Optim, 3 (895-909):
[13] Existence of an optimal solution of a shape control problem for the stationary Navier-Stokes equations
Gunzburger, MD
Kim, H
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1998, 36 (03) : 895 - 909
[14] On optimal control and exact controllability for systems governed by stokes and Navier-Stokes equations
Cao, Y
Hussaini, MY
THIRD INTERNATIONAL CONFERENCE ON NONLINEAR PROBLEMS IN AVIATION AND AEROSPACE, VOLS 1 AND 2, PROCEEDINGS, 2002, : 117 - 126
[15] Second order optimality conditions for periodic optimal control problems governed by semilinear parabolic differential equations
Liu, Hanbing
Wang, Gengsheng
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2021, 27
[16] Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints
B. T. Kien
V. H. Nhu
A. Rösch
Journal of Optimization Theory and Applications, 2015, 165 : 30 - 61
[17] Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints
Kien, B. T.
Nhu, V. H.
Roesch, A.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 165 (01) : 30 - 61
[18] Parallel-in-time multiple shooting for optimal control problems governed by the Navier-Stokes equations
Janssens, N.
Meyers, J.
COMPUTER PHYSICS COMMUNICATIONS, 2024, 296
[19] STABILITY AND ERROR ANALYSIS OF A SECOND-ORDER CONSISTENT SPLITTING SCHEME FOR THE NAVIER-STOKES EQUATIONS
Huang, Fukeng
Shen, Jie
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2023, 61 (05) : 2408 - 2433
[20] Assessment of second-order velocity-slip boundary conditions of the navier-stokes equations
Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Acad. of Sci., Beijing 100080, China
Lixue Xuebao, 2007, 1 (1-6): : 1 - 6

← 1 2 3 4 5 →