Mixed-Integer Nonlinear Programming

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



AuthorTitleYearJournal/ProceedingsReftypeLink
Huschto, T., Podolskij, M., Sager, S. The asymptotic error of chaos expansion approximations for stochastic differential equations 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 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 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 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 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 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 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.

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Prof. Dr. Sebastian Sager
Head of MathOpt group
at the Institute of Mathematical Optimization
at the Faculty of Mathematics
at the Otto-von-Guericke University Magdeburg

Universitätsplatz 2, 02-224
39106 Magdeburg, Germany

: +49 391 67 58745
:

Susanne Heß

Universitätsplatz 2, 02-201
39106 Magdeburg, Germany

: +49 391 67 58756
:

  • currently no upcoming news

...more

Prof. Dr. Sebastian Sager
Head of MathOpt group
at the Institute of Mathematical Optimization
at the Faculty of Mathematics
at the Otto-von-Guericke University Magdeburg

Universitätsplatz 2, 02-224
39106 Magdeburg, Germany

: +49 391 67 58745
:

Susanne Heß

Universitätsplatz 2, 02-201
39106 Magdeburg, Germany

: +49 391 67 58756
: