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Cut Generation for Optimization Problems with Multivariate Risk Constraints

Simge Kucukyavuz (kucukyavuz.2***at***osu.edu)
Nilay Noyan (nnoyan***at***sabanciuniv.edu)

Abstract: We consider a class of multicriteria stochastic optimization problems that features benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixed-integer programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear description of two non-convex substructures appearing in these cut generation problems. We present computational results that show the effectiveness of our proposed models and methods.

Keywords: multicriteria optimization; multiexpert optimization; multivariate risk-aversion; conditional value-at-risk; stochastic dominance; cut generation; stochastic programming; integer programming

Category 1: Stochastic Programming

Category 2: Other Topics (Multi-Criteria Optimization )

Category 3: Integer Programming

Citation: Küçükyavuz S. and N. Noyan, 2016. Cut Generation for Optimization Problems with Multivariate Risk Constraints, Mathematical Programming, 159 (1), 165-199. http://dx.doi.org/10.1007/s10107-015-0953-7


Entry Submitted: 07/26/2014
Entry Accepted: 07/27/2014
Entry Last Modified: 01/19/2018

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