Erratum to: Computational complexity of stochastic programming problems

Computational complexity of stochastic programming problems

Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast amount of literature on the subject has appeared. The researchers in the field have never ceased to emphasize the inherent difficulties in solving stochastic programming problems, without ever giving a theoretical justification of thi...

A comment on "computational complexity of stochastic programming problems"

Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Mathematical Programming A, 106(3):423–432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem da...

On complexity of stochastic programming problems

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 multi-stage stochastic programs, in general, are intractable. We also discuss complexity of chance constrained problems and multi-s...

Computational Complexity of Stochastic Programming: Monte Carlo Sampling Approach

For a long time modeling approaches to stochastic programming were dominated by scenario generation methods. Consequently the main computational effort went into development of decomposition type algorithms for solving constructed large scale (linear) optimization problems. A different point of view emerged recently where computational complexity of stochastic programming problems was investiga...

Complexity of two and multi-stage stochastic programming problems