chance constraints – Page 9 – Optimization Online

Scenario Approximations of Chance Constraints

Published: 2004/11/15

Optimization of Simulated Systems, Stochastic Programming chance constraints, convex optimization, importance sampling, monte carlo sampling, stochastic uncertainty

We consider an optimization problem of minimization of a linear function subject to chance constraints. In the multidimensional case this problem is, generically, a problem of minimizing under a nonconvex and difficult to compute constraints and as such is computationally intractable. We investigate the potential of conceptually simple scenario approximation of the chance constraints. The … Read more

On complexity of stochastic programming problems

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

Arkadi Nemirovski

Alexander Shapiro

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