Optimization under Uncertainty

We are interested in an efficient solution of optimal control problems of dynamic processes under uncertainty. This comprises the inclusion of risk measures, such as worst case, expected value, Value at Risk, or Conditional Value at Risk into the problem formulation. It also comprises optimal control with stochastic differential equations. We have been developing a novel generic methodology to solve continuous finite-horizon stochastic optimal control problems (SOCPs). We treat controlled stochastic differential equations (SDEs) within the Wiener chaos framework by utilizing Malliavin calculus and developing innovative ideas to preserve the feedback character of optimal Markov decision rules. This allows a direct reformulation of SOCPs into deterministic ones. Hence, it facilitates using Bock's direct multiple shooting method for solving SOCPs and pioneers the extension of sophisticated methods for deterministic control to the broad context of SDEs.

Selected publications

2019
article
Huschto, T., Podolskij, M., Sager, S.
The asymptotic error of chaos expansion approximations for stochastic differential equations
Modern Stochastics: Theory and Applications
@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}
}
2017
article
Jost, F., Sager, S., Le, T.
A Feedback Optimal Control Algorithm with Optimal Measurement Time Points
Processes
@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}
}
2017
inproceedings
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
Studies in Computational Intelligence: Complex Networks and Their Applications V
@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}
}
2017
inproceedings
Matke, C., Medjroubi, W., Kleinhans, D., Sager, S.
Structure Analysis of the German Transmission Network Using the Open Source Model SciGRID
Advances in Energy System Optimization
@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}
}
2014
article
Huschto, T., Sager, S.
Pricing Conspicuous Consumption Products in Recession Periods with Uncertain Strength
European Journal of Decision Processes
@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}
}
2014
article
Huschto, T., Sager, S.
Solving Stochastic Optimal Control Problems by a Wiener Chaos Approach
Vietnam Journal of Mathematics
@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}
}
2014
phdthesis
Huschto, T.
Numerical Methods for Random Parameter Optimal Control and the Optimal Control of Stochastic Differential Equations
University Heidelberg
@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}
}
  • currently no upcoming news

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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
: