The Terminator: An Integration of Inner and Outer Approximations for Solving Regular and Distributionally Robust Chance Constrained Programs via Variable Fixing

We present a novel approach aimed at enhancing the efficacy of solving both regular and distributionally robust chance constrained programs using an empirical reference distribution. In general, these programs can be reformulated as mixed-integer programs (MIPs) by introducing binary variables for each scenario, indicating whether a scenario should be satisfied. While existing methods have predominantly … Read more

ALSO-X#: Better Convex Approximations for Distributionally Robust Chance Constrained Programs

This paper studies distributionally robust chance constrained programs (DRCCPs), where the uncertain constraints must be satisfied with at least a probability of a prespecified threshold for all probability distributions from the Wasserstein ambiguity set. As DRCCPs are often nonconvex and challenging to solve optimally, researchers have been developing various convex inner approximations. Recently, ALSO-X has … Read more

Distributionally Favorable Optimization: A Framework for Data-driven Decision-making with Endogenous Outliers

A typical data-driven stochastic program aims to seek the best decision that minimizes the sum of a deterministic cost function and an expected recourse function under a given distribution. Recently, much success has been witnessed in the development of Distributionally Robust Optimization (DRO), which considers the worst-case expected recourse function under the least favorable probability … Read more

ALSO-X and ALSO-X+: Better Convex Approximations for Chance Constrained Programs

In a chance constrained program (CCP), the decision-makers aim to seek the best decision whose probability of violating the uncertainty constraints is within the prespecified risk level. As a CCP is often nonconvex and is difficult to solve to optimality, much effort has been devoted to developing convex inner approximations for a CCP, among which … Read more