Michal Houda

Chance constrained 0–1 quadratic programs using copulas

In this paper, we study 0–1 quadratic programs with joint probabilistic constraints. The row vectors of the constraint matrix are assumed to be normally distributed but are not supposed to be independent. We propose a mixed integer linear reformulation and provide an efficient semidefinite relaxation of the original problem. The dependence of the random vectors is handled by the means of copulas. Finally, numerical experiments are conducted to show the strength of our approach.

A Note on Quantitative Stability and Empirical Estimates in Stochastic Programming

The paper deals with a stability of stochastic programming problems considered with respect to a probability measure space. In particular, the paper deals with the stability of the problems in which the operator of mathematical expectation appears in the objective function, constraints set is “deterministic” and the probability measure space is equipped with the Kolmogorov or the Wasserstein metric. The stability results are furthermore employed to statistical estimates in the stochastic programming problems. Some results on a consistence and a rate of convergence are presented.

On the Use of Copulas in Joint Chance-constrained Programming

In this paper, we investigate the problem of linear joint probabilistic constraints with normally distributed constraints. We assume that the rows of the constraint matrix are dependent, the dependence is driven by a convenient Archimedean copula. We describe main properties of the problem and show how dependence modeled through copulas translates to the model formulation. We also develop an approximation scheme for this class of stochastic programming problems based on second-order cone programming.

Archimedean Copulas in Joint Chance-Constrained Programming

We investigate the problem of linear joint probabilistic constraints with normally distributed constraints in this paper. We assume that the rows of the constraint matrix are dependent, the dependence is driven by a convenient Archimedean copula. We describe main properties of the problem, show how dependence modeled through copulas translates to the model formulation, and prove that the resulting problem is convex for a sufficiently high probability level. We further develop an approximation scheme for this class of stochastic programming problems based on second-order cone programming.