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. Numerical Methods for Random Parameter Optimal Control and the Optimal Control of Stochastic Differential Equations 2014 School: University Heidelberg   phdthesis
preprint  
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://www.mathopt.de/PUBLICATIONS/Huschto2014.pdf}
}
Huschto, T. & Sager, S. Pricing Conspicuous Consumption Products in Recession Periods with Uncertain Strength 2014 European Journal of Decision Processes   article
preprint  
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
preprint  
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 = {http://mathopt.de/PUBLICATIONS/Huschto2014a.pdf}
}

Further references of the MathOpt group can be found on this page.

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