First- and Second-Order Necessary Optimality Conditions for Optimal Control Problems Governed by Stationary Navier–Stokes Equations with Pure State Constraints

被引：3
作者：
Kien B.T. [1 ]
Lee G.M. [2 ]
Son N.H. [3 ]
机构：
[1] Department of Optimization and Control Theory, Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet road, Hanoi
[2] Department of Applied Mathematics, Pukyong National University, Busan
[3] School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi
来源：
Vietnam Journal of Mathematics | 2016年 / 44卷 / 1期
关键词：
First-order optimality condition; Optimal control; Pontryagin’s principle; Pure state constraint; Second-order optimality condition; The stationary Navier–Stokes equations;
D O I：
10.1007/s10013-015-0173-8
中图分类号：
学科分类号：
摘要：
Based on tools of variational analysis and the diffuse variation method, we derive the Pontryagin maximum principle and second-order necessary optimality conditions for optimal control problems governed by stationary Navier–Stokes equations with pure state constraints. Our results are established under a smallness assumption on the control and the optimality conditions are of Fritz–John type. © 2015, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
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页码：103 / 131
页数：28
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