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TITLE: On Deterministic Reformulations of Distributionally Robust Chance Constrained Program
ABSTRACT:
A chance constrained optimization problem involves multiple uncertain constraints, i.e. constraints with stochastic parameters, that are required to be satisfied with probability at least a pre-specified threshold. In a distributionally robust chance constrained program (DRCCP), the chance constraint is required to hold for all probability distributions of the stochastic parameters from a given family of distributions, called an ambiguity set. In this work, we consider DRCCP involving linear uncertain constraints and an ambiguity set specified by convex moment inequalities. In general, a DRCCP is nonconvex and hence NP-hard to optimize. We develop deterministic reformulations of such problems and establish sufficient conditions under which these formulations are convex and tractable. We further approximate DRCCP by a system of single chance constraints, one for each uncertain constraint. The tractability of such approximation has been “an open question” since 2006. We provide sufficient conditions under which the approximation set is equivalent to the feasible region of DRCCP and can be reformulated as a convex program. Finally, we present a chance constrained optimal power flow model to illustrate the proposed methodology.
