Monte Carlo sampling approach to stochastic programming

Computational Complexity of Stochastic Programming: Monte Carlo Sampling Approach

For a long time modeling approaches to stochastic programming were dominated by scenario generation methods. Consequently the main computational effort went into development of decomposition type algorithms for solving constructed large scale (linear) optimization problems. A different point of view emerged recently where computational complexity of stochastic programming problems was investiga...

The Markov Chain Monte Carlo Approach to Importance Sampling in Stochastic Programming

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 involves the evaluation of a multidimensional inte...

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

Stochastic programming models are large-scale optimization problems that are used to facilitate decisionmaking 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 integ...

Monte Carlo sampling for stochastic weight functions.

Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here, we consider the case that the weight determining the acceptance probability itself is fluctuating. This situation is common in many numerical studies. We show that it is p...

Stochastic Methods: Monte Carlo Approach