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.

引用

页码：103 / 131

页数：28

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