two-stage stochastic programming – Page 3

On complexity of Shmoys – Swamy class of two-stage linear stochastic programming problems

Published: 2006/07/28

Approximation Algorithms, Stochastic Programming complexity, set cover problem, two-stage stochastic programming

We consider a class of two-stage linear stochastic programming problems, introduced by Shmoys and Swamy (2004), motivated by a relaxation of a stochastic set cover problem. We show that the sample size required to solve this problem by the sample average approximation (SAA) method with a relative accuracy $\kappa>0$ and confidence $1-\alpha$ is polynomial in … Read more

Stochastic Programming with Equilibrium Constraints

Published: 2004/08/06, Updated: 2005/01/17

Alexander Shapiro

Complementarity and Variational Inequalities, Stochastic Programming complementarity conditions, equilibrium constraints, exponential rates, statistical inference, statistical variational inequalities, two-stage stochastic programming, variational inequality

In this paper we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We also discuss consistency and rates of convergence of sample average approximations of such stochastic problems. CitationSchool of Industrial and … Read more