two-stage stochastic programming

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

  • Arkadi Nemirovski
  • Alexander Shapiro
    • Categories Approximation Algorithms, Stochastic Programming Tags , ,

    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

  • Alexander Shapiro
    • Categories Complementarity and Variational Inequalities, Stochastic Programming Tags , , , , , ,

    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. Citation School of Industrial … Read more