Chance-constrained problems and rare events: an importance sampling approach

We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. Using a Sample Average Approximation (SAA) approach … Read more

Risk-Averse Stochastic Dual Dynamic Programming

We formulate a risk-averse multi-stage stochastic program using conditional value at risk as the risk measure. The underlying random process is assumed to be stage-wise independent, and a stochastic dual dynamic programming (SDDP) algorithm is applied. We discuss the poor performance of the standard upper bound estimator in the risk-averse setting and propose a new … Read more

Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach

Stochastic programming models are large-scale optimization problems that are used to facilitate decision-making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integral whose integrand … Read more

Scenario Approximations of Chance Constraints

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