Chance constrained nonlinear optimization with skewed distributions and dependent rows

This paper discusses chance constrained optimization problems where the constraints are linear to the random variables but nonlinear to the decision variables. For the individual nonlinear chance constraint, we derive tractable reformulation under finite Gaussian mixture distributions and design tight approximation under the generalized hyperbolic distribution. For the joint nonlinear chance constraint, we study several … Read more

Distributionally robust second-order stochastic dominance constrained optimization with Wasserstein distance

We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the empirical distribution. We adopt the sample approximation approach to develop a linear programming formulation that provides a lower bound. We propose a novel split-and-dual decomposition … Read more

Distributionally robust chance constrained geometric optimization

This paper discusses distributionally robust geometric programs with individual and joint chance constraints. Seven groups of uncertainty sets are considered: uncertainty sets with first two order moments information, uncertainty sets constrained by the Kullback-Leibler divergence distance with a normal reference distribution or a discrete reference distribution, uncertainty sets with known first moments or known first … Read more