Optimal control problems with control complementarity constraints: existence results, optimality conditions, and a penalty method. (2nd January 2020)

• Record Type: Journal Article
• Authors: Clason, Christian; Deng, Yu; Mehlitz, Patrick; Prüfert, Uwe
• Is Part Of: Optimization methods and software. Volume 35:Number 1(2020)
• Page Start: 142
• Page End: 170
• Publication Date: 2020-01-02
• Subjects: Fischer–Burmeister function -- mathematical problems with complementarity constraints -- optimal control -- optimality conditions -- penalty method; 49J20 -- 49K20 -- 49M05 -- 49M25 -- 90C48; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1604705
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space. After deriving necessary optimality conditions of strong stationarity-type, a penalty method based on the Fischer–Burmeister function is suggested and its theoretical properties are analyzed. Finally, the numerical treatment of the problem is discussed and results of computational experiments are presented.