Mathematical programming approaches for generating pefficient points
Lejeune, Miguel and Noyan, Nilay (2009) Mathematical programming approaches for generating pefficient points. (Submitted) AbstractPefficient points (pLEPs), introduced by Prekopa (1990), are utilized to solve probabilistically constrained problems which have been receiving significant attention in a wide range of application fields. Due to their nonconvex feasible regions such problems are hard to solve. In a special case, the
probabilistic constraint is enforced jointly on constraints involving randomness only in the right hand side and the vector of random variables has a finite distribution. For this special class of problems, the concept of the pefficient point has been widely used to develop associated ecient solution methods.
Those methods require the generation of pLEPs. We consider a finite random vector that is characterized by a set of scenarios and propose a mathematical programming based approach to generate pLEPs. Using a mixedinteger formulation, we obtain a method to generate pLEPs based on a new preprocessing technique and iterative outer approximations. Moreover, some valid inequalities are derived to strengthen the formulations of the outer approximations, which result in improved computational performance of the proposed generation method. We also develop a heuristic algorithm to generate “quasi pLEPs” efficiently. To the best of our knowledge, developing an optimizationbased approach for generating multiple pLEPs and developing a method for generating pLEPs for random variables characterized by a set of scenarios are novel. We also present some numerical
results to show the computational efficiency and effectiveness of the proposed methods. Item Type:  Article 

Uncontrolled Keywords:  Stochastic programming, probabilistic constraints, peciency, outer approximation 

Subjects:  Q Science > Q Science (General) 

ID Code:  13220 

Deposited By:  Nilay Noyan 

Deposited On:  04 Dec 2009 11:38 

Last Modified:  13 Oct 2010 10:49 

Available Versions of this Item Mathematical programming approaches for generating pefficient points. (deposited 04 Dec 2009 11:38) [Currently Displayed]
Repository Staff Only: item control page
