Study of stochastic bilevel programming with applications to energy management and network design problems.
Context
The research topic is Stochastic Combinatorial Bilevel Optimization Problems with equilibrium constraints, which is at the crossroads between probability theory, discrete mathematics, convex optimization, game theory and computer science. The project aims at developing new and fast methods for finding exact or approximate solutions to hard stochastic combinatorial bilevel optimization problems with equilibrium constraints.
Stochastic bilevel programming problems are commonly solved using Generalized Linear Complementarity Problems (GLCP for short) based on the optimality conditions for the follower problem. GLCP are nonlinear and generally non convex problems which make them very hard to deal with both from theoretical and practical point of view. This new topic needs advanced theoretical studies in order to propose new efficient methods and algorithms for solving stochastic combinatorial bilevel optimization problems.
Objectives
Our objectives in this projet are fourfold:
1.Study new algorithms based on stochastic gradient methods for solving stochastic bilevel combinatorial optimization problems with equilibrium constraints.
2. Application of such algorithms for solving stochastic bilevel combinatorial optimization problems. Both theoritical and algorithmic aspects will be considered.
3. Derive tight bounds and efficient algorithms for such problems.
4. Applications will be considered in the area of network design problems and energy planning problems.
Work program
The candidate will work on the approaches developed within GraphComb team, namely GLCP methods, stochastic gradient methods with continuous distributions as well as the state of the art in stochastic programming. Special interest will be given to chance constraint problems together with bilevel optimization.
Extra information
Prerequisite
The candidate should have a strong background in mathematics in general and more specifically in probability theory, statistics and optimization. Skills in computer science are appreciated.
Détails
Expected funding
Institutional funding
Status of funding
Expected
Candidates
Utilisateur
abdel.lisser
Créé
Mercredi 30 mars 2011 23:04:16 CEST
dernière modif.
Jeudi 10 mai 2012 09:53:16 CEST
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Connexion
Ecole Doctorale Informatique Paris-Sud
Directrice
Nicole Bidoit Assistante
Stéphanie Druetta Conseiller aux thèses
Dominique Gouyou-Beauchamps
ED 427 - Université Paris-Sud
UFR Sciences Orsay
Bat 650 - aile nord - 417
Tel : 01 69 15 63 19
Fax : 01 69 15 63 87
courriel: ed-info à lri.fr