Scenario reduction for stochastic programs with Conditional Value-at-Risk
- 16 Downloads
In this paper we discuss scenario reduction methods for risk-averse stochastic optimization problems. Scenario reduction techniques have received some attention in the literature and are used by practitioners, as such methods allow for an approximation of the random variables in the problem with a moderate number of scenarios, which in turn make the optimization problem easier to solve. The majority of works for scenario reduction are designed for classical risk-neutral stochastic optimization problems; however, it is intuitive that in the risk-averse case one is more concerned with scenarios that correspond to high cost. By building upon the notion of effective scenarios recently introduced in the literature, we formalize that intuitive idea and propose a scenario reduction technique for stochastic optimization problems where the objective function is a Conditional Value-at-Risk. Numerical results presented with problems from the literature illustrate the performance of the method and indicate the cases where we expect it to perform well.
Mathematics Subject Classification90C15 (Stochastic Programming) 90C31 (Sensitivity, stability, parametric optimization) 90C59 (Approximation methods and heuristics)
We thank the anonymous referees for their constructive comments which helped improve the presentation of our results. This work has been supported by FONDECYT 1171145, Chile.
- 2.Altenstedt, F.: Aspects on Asset Liability Management Via Stochastic Programming. Chalmers University of Technology, Gothenburg (2003)Google Scholar
- 9.Dolan, E.D.: The neos server 4.0 administrative guide (Technical Memorandum NO. ANL/MCS-TM-250). Mathematics and Computer Science Division, Argonne National Laboratory (2001)Google Scholar
- 15.Fairbrother, J., Turner, A., Wallace, S.: Scenario generation for stochastic programs with tail risk measures (2015). arXiv preprint arXiv:1511.03074
- 18.Gropp, W., Moré, J.J.: Optimization environments and the neos server. In: Buhman, Martin D., Iserles, Arieh (eds.) Approximation Theory and Optimization, pp. 167–182. Cambridge University Press, Cambridge (1997)Google Scholar
- 19.Guigues, V., Krätschmer, V., Shapiro, A.: Statistical inference and hypotheses testing of risk averse stochastic programs (2016). arXiv preprint arXiv:1603.07384
- 26.Louveaux, F., Smeers, Y.: Optimal investments for electricity generation: a stochastic model and a test problem. In: Ermoliev, Y., Wets, R.J.-B. (eds.) Numericaltechniques for Stochastic Optimization Problems, pp. 445–452. Springer, Berlin (1988)Google Scholar
- 35.Rahimian, H., Bayraksan, G., Homem-de Mello, T.: Identifying effective scenarios in distributionally robust stochastic programs with total variation distance. Math. Program. (2018). https://doi.org/10.1007/s10107-017-1224-6