@misc{BenitaMehlitz, author = {Benita, Francisco and Mehlitz, Patrick}, title = {Optimal Control Problems with Terminal Complementarity Constraints}, series = {SIAM Journal on Optimization (SIOPT)}, volume = {28}, journal = {SIAM Journal on Optimization (SIOPT)}, number = {4}, issn = {1052-6234}, doi = {10.1137/16M107637X}, pages = {3079 -- 3104}, abstract = {In this paper, we study an optimal control problem of ordinary differential equations with linear dynamics, affine mixed control-state constraints, and terminal complementarity constraints on the state function. We derive its weak, Mordukhovich, and strong stationarity conditions, and we present constraint qualifications which ensure that these conditions are satisfied at a locally optimal solution of the optimal control problem.}, language = {en} } @misc{BenitaDempeMehlitz, author = {Benita, Francisco and Dempe, Stephan and Mehlitz, Patrick}, title = {Bilevel Optimal Control Problems with Pure State Constraints and Finite-dimensional Lower Level}, series = {SIAM Journal on Optimization (SIOPT)}, volume = {26}, journal = {SIAM Journal on Optimization (SIOPT)}, number = {1}, issn = {1052-6234}, doi = {10.1137/141000889}, pages = {564 -- 588}, abstract = {This paper focuses on the development of optimality conditions for a bilevel optimal control problem with pure state constraints in the upper level and a finite-dimensional parametric optimization problem in the lower level. After transforming the problem into an equivalent single-level problem, we concentrate on the derivation of a necessary optimality condition of Pontryagin type. We point out some major difficulties arising from the bilevel structure of the original problem and its pure state constraints in the upper level leading to a degenerated maximum principle in the absence of constraint qualifications. Hence, we use a partial penalization approach and a well-known regularity condition for optimal control problems with pure state constraints to ensure the nondegeneracy of the derived maximum principle. Finally, we illustrate the applicability of the derived theory by means of a small example.}, language = {en} } @misc{BenitaMehlitz, author = {Benita, Francisco and Mehlitz, Patrick}, title = {Bilevel Optimal Control With Final-State-Dependent Finite-Dimensional Lower Level}, series = {SIAM Journal on Optimization (SIOPT)}, volume = {26}, journal = {SIAM Journal on Optimization (SIOPT)}, number = {1}, issn = {1052-6234}, doi = {10.1137/15M1015984}, pages = {718 -- 752}, abstract = {In this paper we discuss special bilevel optimal control problems where the upper level problem is an optimal control problem of ODEs with control and terminal constraints and the lower level problem is a finite-dimensional parametric optimization problem where the parameter is the final state of the state variable of the upper level. We tackle this problem using tools from nonsmooth analysis, optimization in Banach spaces, and bilevel programming to derive necessary optimality conditions of linearized Pontryagin-type.}, language = {en} } @misc{BenitaMehlitz, author = {Benita, Francisco and Mehlitz, Patrick}, title = {Solving optimal control problems with terminal complementarity constraints via Scholtes' relaxation scheme}, series = {Computational Optimization and Applications : (COAP)}, volume = {72}, journal = {Computational Optimization and Applications : (COAP)}, number = {2}, issn = {0926-6003}, doi = {10.1007/s10589-018-0050-y}, pages = {413 -- 430}, abstract = {We investigate the numerical treatment of optimal control problems of linear ordinary differential equations with terminal complementarity constraints. Therefore, we generalize the well-known relaxation technique of Scholtes to the problem at hand. In principle, any other relaxation approach from finite-dimensional complementarity programming can be adapted in similar fashion. It is shown that the suggested method possesses strong convergence properties under mild assumptions. Finally, some numerical examples are presented.}, language = {en} }