caa a22 4500 445839732 CHVBK 20180317145340.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00186-011-0355-4 doi (NATIONALLICENCE)springer-10.1007/s00186-011-0355-4 Combinatorial integral approximation [Elektronische Daten] [Sebastian Sager, Michael Jung, Christian Kirches] We are interested in structures and efficient methods for mixed-integer nonlinear programs (MINLP) that arise from a first discretize, then optimize approach to time-dependent mixed-integer optimal control problems (MIOCPs). In this study we focus on combinatorial constraints, in particular on restrictions on the number of switches on a fixed time grid. We propose a novel approach that is based on a decomposition of the MINLP into a NLP and a MILP. We discuss the relation of the MILP solution to the MINLP solution and formulate bounds for the gap between the two, depending on Lipschitz constants and the control discretization grid size. The MILP solution can also be used for an efficient initialization of the MINLP solution process. The speedup of the solution of the MILP compared to the MINLP solution is considerable already for general purpose MILP solvers. We analyze the structure of the MILP that takes switching constraints into account and propose a tailored Branch and Bound strategy that outperforms cplex on a numerical case study and hence further improves efficiency of our novel method. Springer-Verlag, 2011 MINLP nationallicence MIOCP nationallicence MILP nationallicence Optimal control nationallicence Integer programming nationallicence Sager Sebastian Interdisciplinary Center for Scientific Computing, University of Heidelberg, INF 368, 69120, Heidelberg, Germany aut Jung Michael Interdisciplinary Center for Scientific Computing, University of Heidelberg, INF 368, 69120, Heidelberg, Germany aut Kirches Christian Interdisciplinary Center for Scientific Computing, University of Heidelberg, INF 368, 69120, Heidelberg, Germany aut Mathematical Methods of Operations Research Springer-Verlag 73/3(2011-06-01), 363-380 1432-2994 73:3<363 2011 73 186 https://doi.org/10.1007/s00186-011-0355-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00186-011-0355-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sager Sebastian Interdisciplinary Center for Scientific Computing, University of Heidelberg, INF 368, 69120, Heidelberg, Germany aut NATIONALLICENCE 700 1- Jung Michael Interdisciplinary Center for Scientific Computing, University of Heidelberg, INF 368, 69120, Heidelberg, Germany aut NATIONALLICENCE 700 1- Kirches Christian Interdisciplinary Center for Scientific Computing, University of Heidelberg, INF 368, 69120, Heidelberg, Germany aut NATIONALLICENCE 773 0- Mathematical Methods of Operations Research Springer-Verlag 73/3(2011-06-01), 363-380 1432-2994 73:3<363 2011 73 186 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer