Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations

被引：60

作者：

Tröltzsch, F ^{[1
]}

Wachsmuth, D ^{[1
]}

机构：

[1] Tech Univ Berlin, Inst Math, D-10632 Berlin, Germany

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2006年 / 12卷 / 01期

关键词：

optimal control; Navier-Stokes equations; control constraints; second-order optimality conditions; first-order necessary conditions;

D O I：

10.1051/cocv:2005029

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a L-s-neighborhood, whereby the underlying analysis allows to use weaker norms than L-infinity.

引用

页码：93 / 119

页数：27

共 28 条

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Abergel F., 1990, THEOR COMP FLUID DYN, V1, P303, DOI [DOI 10.1007/BF00271794, 10.1007/bf00271794]

[2]

Adams R, 1978, Sobolev spaces

[3] On an augmented Lagrangian SQP method for a class of optimal control problems in Banach spaces [J].