Cut generation for optimization problems with multivariate risk constraints

Küçükyavuz, Simge and Noyan, Nilay (2016) Cut generation for optimization problems with multivariate risk constraints. Mathematical Programming, 159 (1). pp. 165-199. ISSN 0025-5610 (Print) 1436-4646 (Online)

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Official URL: http://dx.doi.org/10.1007/s10107-015-0953-7


We consider a class of stochastic optimization problems that features benchmarking preference relations among random vectors representing multiple random performance measures (criteria) of interest. Given a benchmark random performance vector, preference relations are incorporated into the model as constraints, which require the decision-based random vector to be preferred to the benchmark according to a relation based on multivariate conditional value-at-risk (CVaR) or second-order stochastic dominance (SSD). We develop alternative mixed-integer programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. The cut generation problems for CVaR- and SSD-based models involve the epigraphs of two distinct piecewise linear concave functions, which we refer to as reverse concave sets. We give the complete linear description of the linearization polytopes of these two non-convex substructures. We present computational results that show the effectiveness of our proposed models and methods.

Item Type:Article
Uncontrolled Keywords:Stochastic programming, Multivariate risk-aversion, Conditional value-at-risk, Stochastic dominance, Cut generation, Convex hull, Reverse concave set
Subjects:Q Science > Q Science (General)
ID Code:29805
Deposited By:Nilay Noyan
Deposited On:09 Nov 2016 14:15
Last Modified:09 Nov 2016 14:15

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