Constraint generation for risk averse two-stage stochastic programs

A significant share of stochastic optimization problems in practice can be cast as two-stage stochastic programs. If uncertainty is available through a finite set of scenarios, which frequently occurs, and we are interested in accounting for risk aversion, the expectation in the recourse cost can be replaced with a worst-case function (i.e., robust optimization) or another risk-functional, such as conditional value-at-risk. In this paper we are interested in the latter situation especially when the number of scenarios is large. For computational efficiency we suggest a (clustering and) constraint generation algorithm. We establish convergence of these two algorithms and demonstrate their effectiveness through various numerical experiments. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

Many practical stochastic optimization problems can be formulated as two-stage stochastic programs, and in situations where risk aversion is of interest, methods such as robust optimization or other risk-functional approaches can be used. This paper focuses on the latter case, particularly when there is a large number of scenarios, proposing a constraint generation algorithm for computational efficiency. The convergence of these algorithms is established and their effectiveness is demonstrated through various numerical experiments.