monte carlo sampling – Page 2 – Optimization Online

On complexity of stochastic programming problems

Published: 2004/10/09, Updated: 2005/01/15

Stochastic Programming chance constraints, complete recourse, convex optimization, large deviations bounds, monte carlo sampling, multi-stage stochastic programming, saa method, stochastic programming

The main focus of this paper is 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-stage … Read more

Statistical inference of multistage stochastic programming problems

Published: 2002/01/18

Alexander Shapiro

Stochastic Programming consistent estimators, monte carlo sampling, multistage stochastic programs with recourse, statistical bounds, stochastic programming

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. … Read more