SECOND ORDER SUFFICIENT OPTIMALITY CONDITIONS FOR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH POINTWISE STATE CONSTRAINTS

被引：27

作者：

Krumbiegel, K. ^{[1
]}

Rehberg, J. ^{[1
]}

机构：

[1] Weierstrass Inst Appl Math & Stochast, D-10117 Berlin, Germany

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 01期

关键词：

parabolic equation; maximal parabolic regularity; optimal control; sufficient optimality conditions; ELLIPTIC TRANSMISSION PROBLEMS; BOUNDARY-VALUE-PROBLEMS; REGULARITY; STABILITY; 1ST;

D O I：

10.1137/120871687

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 we study optimal control problems governed by semilinear parabolic equations where the spatial dimension is two or three. Moreover, we consider pointwise constraints on the control and on the state. We formulate first order necessary and second order sufficient optimality conditions. We make use of recent results regarding elliptic regularity and apply the concept of maximal parabolic regularity to the occurring partial differential equations.

引用

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页码：304 / 331

页数：28

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