Bilevel programming problems with simple convex lower level. (2nd June 2016)

• Record Type: Journal Article
• Authors: Mehlitz, Patrick
• Is Part Of: Optimization. Volume 65:Number 6(2016)
• Page Start: 1203
• Page End: 1227
• Publication Date: 2016-06-02
• Subjects: Bilevel programming -- optimization in Banach spaces -- nonsmooth optimization -- DC-programming -- optimal control; 49J15 -- 90C25 -- 90C47 -- 90C48 -- 90C56; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1122006
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This article is dedicated to the study of bilevel optimal control problems equipped with a fully convex lower level of special structure. In order to construct necessary optimality conditions, we consider a general bilevel programming problem in Banach spaces possessing operator constraints, which is a generalization of the original bilevel optimal control problem. We derive necessary optimality conditions for the latter problem using the lower level optimal value function, ideas from DC-programming and partial penalization. Afterwards, we apply our results to the original optimal control problem to obtain necessary optimality conditions of Pontryagin-type. Along the way, we derive a handy formula, which might be used to compute the subdifferential of the optimal value function which corresponds to the lower level parametric optimal control problem.