Chapter

Continuous Optimization

Volume 99 of the series Applied Optimization pp 111-146

On Complexity of Stochastic Programming Problems

  • Alexander ShapiroAffiliated withGeorgia Institute of Technology
  • , Arkadi NemirovskiAffiliated withTechnion — Israel Institute of Technology

Summary

The main focus of this paper is in a discussion of complexity of stochastic programming problems. We argue that two-stage (linear) stochastic programming problems with recourse can be solved with a reasonable accuracy by using Monte Carlo sampling techniques, while multistage stochastic programs, in general, are intractable. We also discuss complexity of chance constrained problems and multistage stochastic programs with linear decision rules.

Key words

stochastic programming complete recourse chance constraints Monte Carlo sampling SAA method large deviations bounds convex programming multi-stage stochastic programming