We are particularly 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). We focus, e.g., on combinatorial constraints such as 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 state-of-the-art solvers on a numerical case study.
Selected publications
| Author | Title | Year | Journal/Proceedings | Reftype | Link |
|---|---|---|---|---|---|
| Huschto, T., Podolskij, M., Sager, S. | The asymptotic error of chaos expansion approximations for stochastic differential equations [BibTeX] |
2019 | Modern Stochastics: Theory and Applications | article | DOI |
BibTeX:
@article{Huschto2019,
author = {Huschto, T. and Podolskij, M. and Sager, S.},
title = {The asymptotic error of chaos expansion approximations for stochastic differential equations},
journal = {Modern {S}tochastics: {T}heory and {A}pplications},
year = {2019},
volume = {6},
number = {2},
pages = {145--165},
doi = {10.15559/19-VMSTA133}
} |
|||||
| Jost, F., Sager, S., Le, T. | A Feedback Optimal Control Algorithm with Optimal Measurement Time Points [BibTeX] |
2017 | Processes | article | url |
BibTeX:
@article{Jost2017,
author = {Jost, F. and Sager, S. and Le, T.T.T.},
title = {A Feedback Optimal Control Algorithm with Optimal Measurement Time Points},
journal = {Processes},
year = {2017},
volume = {5},
number = {10},
pages = {1--19},
url = {http://www.mdpi.com/2227-9717/5/1/10}
} |
|||||
| Matke, C., Bienstock, D., Munoz, G., Yang, S., Kleinhans, D., Sager, S. | Robust optimization of power network operation: storage devices and the role of forecast errors in renewable energies [BibTeX] |
2017 | Studies in Computational Intelligence: Complex Networks and Their Applications V | inproceedings | DOI |
BibTeX:
@inproceedings{Matke2017,
author = {Matke, C. and Bienstock, D. and Munoz, G. and Yang, S. and Kleinhans, D. and Sager, S.},
title = {Robust optimization of power network operation: storage devices and the role of forecast errors in renewable energies},
booktitle = {Studies in Computational Intelligence: Complex Networks and Their Applications V},
year = {2017},
number = {693},
pages = {809--820},
doi = {10.1007/978-3-319-50901-3}
} |
|||||
| Matke, C., Medjroubi, W., Kleinhans, D., Sager, S. | Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID [BibTeX] |
2017 | Advances in Energy System Optimization | inproceedings | |
BibTeX:
@inproceedings{Matke2017a,
author = {Matke, Carsten and Medjroubi, Wided and Kleinhans, David and Sager, Sebastian},
title = {Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID},
booktitle = {Advances in Energy System Optimization},
publisher = {Springer International Publishing},
year = {2017},
editor = {Bertsch, Valentin and Fichtner, Wolf and Heuveline, Vincent and Leibfried, Thomas},
pages = {177--188},
address = {Cham}
} |
|||||
| Huschto, T., Sager, S. | Pricing Conspicuous Consumption Products in Recession Periods with Uncertain Strength [BibTeX] |
2014 | European Journal of Decision Processes | article | url |
BibTeX:
@article{Huschto2014,
author = {Huschto, T. and Sager, S.},
title = {{P}ricing {C}onspicuous {C}onsumption {P}roducts in {R}ecession {P}eriods with {U}ncertain {S}trength},
journal = {{E}uropean {J}ournal of {D}ecision {P}rocesses},
year = {2014},
volume = {2},
number = {1--2},
pages = {3--30},
url = {http://www.optimization-online.org/DB_HTML/2012/09/3620.html}
} |
|||||
| Huschto, T., Sager, S. | Solving Stochastic Optimal Control Problems by a Wiener Chaos Approach [BibTeX] |
2014 | Vietnam Journal of Mathematics | article | url |
BibTeX:
@article{Huschto2014a,
author = {Huschto, T. and Sager, S.},
title = {{S}olving {S}tochastic {O}ptimal {C}ontrol {P}roblems by a {W}iener {C}haos {A}pproach},
journal = {{V}ietnam {J}ournal of {M}athematics},
year = {2014},
volume = {42},
number = {1},
pages = {83--113},
url = {https://mathopt.de/publications/Huschto2014a.pdf}
} |
|||||
| Huschto, T. | Numerical Methods for Random Parameter Optimal Control and the Optimal Control of Stochastic Differential Equations [BibTeX] |
2014 | School: University Heidelberg | phdthesis | url |
BibTeX:
@phdthesis{Huschto2014b,
author = {Huschto, T.},
title = {{N}umerical {M}ethods for {R}andom {P}arameter {O}ptimal {C}ontrol and the {O}ptimal {C}ontrol of {S}tochastic {D}ifferential {E}quations},
school = {University Heidelberg},
year = {2014},
url = {https://mathopt.de/publications/Huschto2014.pdf}
} |
|||||
Further references of the MathOpt group can be found on this page.