The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems

Abstract EN

We investigate the stochastic linear complementarity problem affinelyaffected by the uncertain parameters.

Assuming that we have only limitedinformation about the uncertain parameters, such as the first two moments or the first two moments as well as the support of the distribution, we formulate the stochastic linear complementarityproblem as a distributionally robust optimization reformation which minimizesthe worst case of an expected complementarity measure with nonnegativityconstraints and a distributionally robust joint chance constraint representingthat the probability of the linear mapping being nonnegative is not less thana given probability level.

Applying the cone dual theory and S-procedure, weshow that the distributionally robust counterpart of the uncertain complementarityproblem can be conservatively approximated by the optimization withbilinear matrix inequalities.

Preliminary numerical results show that a solutionof our method is desirable.