Distributionally Robust Joint Chance-Constrained Programming with Wasserstein Metric

TL;DR

This paper introduces a new exact reformulation and a convex approximation for distributionally robust joint chance-constrained programming using Wasserstein ambiguity sets, improving computational tractability and solution quality.

Contribution

It develops a novel worst-case CVaR approximation model that can be reformulated as a biconvex optimization problem and further relaxed into a convex form, especially for affine constraints.

Findings

The proposed models are computationally effective.

The convex relaxation outperforms existing methods.

The approach is particularly tractable for affine constraints.

Abstract

In this paper, we develop an exact reformulation and a deterministic approximation for distributionally robust joint chance-constrained programmings (DRCCPs) with a general class of convex uncertain constraints under data-driven Wasserstein ambiguity sets. It is known that robust chance constraints can be conservatively approximated by worst-case conditional value-at-risk (CVaR) constraints. It is shown that the proposed worst-case CVaR approximation model can be reformulated as an optimization problem involving biconvex constraints for joint DRCCP. We then derive a convex relaxation of this approximation model by constructing new decision variables which allows us to eliminate biconvex terms. Specifically, when the constraint function is affine in both the decision variable and the uncertainty, then the resulting approximation model is equivalent to a tractable mixed-integer convex reformulation for joint binary DRCCP. Numerical results illustrate the computational effectiveness and superiority of the proposed formulations.