  


A cutting surface algorithm for semiinfinite convex programming with an application to moment robust optimization
Sanjay Mehrotra (mehrotraiems.northwestern.edu) Abstract: We first present and analyze a central cutting surface algorithm for general semiinfinite convex optimization problems, and use it to develop an algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. The cutting surface algorithm is also applicable to problems with nondifferentiable semiinfinite constraints indexed by an infinitedimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of the central cutting surface algorithm even in the solution of traditional semiinfinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. Our primary motivation for the higher level of generality is to solve distributionally robust optimization problems with moment uncertainty. After the analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date. Keywords: semiinfinite programming, robust optimization, stochastic programming, moment matching, column generation, cutting surface methods, cutting plane methods, moment problem Category 1: Infinite Dimensional Optimization (Semiinfinite Programming ) Category 2: Robust Optimization Category 3: Stochastic Programming Citation: Unpublished; submitted for publication. Download: [PDF] Entry Submitted: 06/14/2013 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  