Mathematical Algorithmic Optimization - Otto-von-Guericke-University Magdeburg

 
 
 
 
 
 
 
 

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



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 = {http://dx.doi.org/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 = {http://dx.doi.org/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 = {T. Huschto and S. Sager},
  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.

Last Modification: 2016-05-12 - Contact Person: Sebastian Sager - Impressum