TOPICS IN STOCHASTIC OPTIMIZATION: AND EQUILIBRIUM PROBLEMS - Couverture souple

A. Kulkarni, Ankur

 
9783639180633: TOPICS IN STOCHASTIC OPTIMIZATION: AND EQUILIBRIUM PROBLEMS
Couverture souple
ISBN 10 : 3639180631 ISBN 13 : 9783639180633
Editeur : VDM Verlag, 2009

Synopsis

Stochastic programs form a class of optimization problems that have seen much attention in the last decade. As has the class of equilibrium problems which have resulted largely from the analytic treatment of Nash games. This thesis delves into some challenging areas of stochastic optimization and stochastic equilibrium programming. Our interest is in understanding properties of these problems and in developing algorithms for solving such problems. We first consider a two-period stochastic nonlinear program. In this context, we obtain new insights into the notions of feasibility and recourse for such programs and develop an algorithm based on sequential quadratic programming. The algorithm uses two quadratic programming solvers based on Benders decomposition: an inexact cut version of the L-shaped method and a trust-region method. We next consider stochastic equilibrium problems arising from Nash-Cournot competition, inspired by a Cournot bidding model for electricity markets. We first show existence and uniqueness of Nash equilibria to a wide class of stochastic quadratic games and then develop a splitting method that can be decomposed scenario-wise to compute such equilibria.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Stochastic programs form a class of optimization problems that have seen much attention in the last decade. As has the class of equilibrium problems which have resulted largely from the analytic treatment of Nash games. This thesis delves into some challenging areas of stochastic optimization and stochastic equilibrium programming. Our interest is in understanding properties of these problems and in developing algorithms for solving such problems. We first consider a two-period stochastic nonlinear program. In this context, we obtain new insights into the notions of feasibility and recourse for such programs and develop an algorithm based on sequential quadratic programming. The algorithm uses two quadratic programming solvers based on Benders decomposition: an inexact cut version of the L-shaped method and a trust-region method. We next consider stochastic equilibrium problems arising from Nash-Cournot competition, inspired by a Cournot bidding model for electricity markets. We first show existence and uniqueness of Nash equilibria to a wide class of stochastic quadratic games and then develop a splitting method that can be decomposed scenario-wise to compute such equilibria.

Biographie de l'auteur

Ankur was born in Mumbai, India in 1983. He received his B.Tech. in Aerospace Engineering from the Indian Institute of Technology, Bombay in 2006 and is pursuing a Ph.D. in Industrial Engineering at the University of Illinois, Urbana-Champaign. His research interests are in game theory, mathematical programming, economics and applied probability.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag
Date d'édition
2009
Langue
anglais
ISBN 10 
3639180631
ISBN 13 
9783639180633
Reliure
Broché
Nombre de pages
120
Coordonnées du fabricant
non disponible
Personne responsable
non disponible