Convexity and decomposition of mean-risk stochastic programs |
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Authors: | Shabbir Ahmed |
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Institution: | (1) School of Industrial & Systems Engineering, Georgia Institute of Technology, , 765 Ferst Drive, Atlanta, GA 30332, USA |
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Abstract: | Traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation
criterion. A common approach to addressing risk in decision making problems is to consider a weighted mean-risk objective,
where some dispersion statistic is used as a measure of risk. We investigate the computational suitability of various mean-risk
objective functions in addressing risk in stochastic programming models. We prove that the classical mean-variance criterion
leads to computational intractability even in the simplest stochastic programs. On the other hand, a number of alternative
mean-risk functions are shown to be computationally tractable using slight variants of existing stochastic programming decomposition
algorithms. We propose decomposition-based parametric cutting plane algorithms to generate mean-risk efficient frontiers for
two particular classes of mean-risk objectives. |
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Keywords: | Stochastic programming Mean-risk objectives Computational complexity Decomposition Cutting plane algorithms |
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