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

In a chance constrained program (CCP), decision makers seek the best whose probability of violating uncertainty constraints is within prespecified risk level. As CCP often nonconvex and difficult to solve optimality, much effort has been devoted developing convex inner approximations for CCP, among which conditional value-at-risk ([Formula: see text]) known be more than decade. This paper studies generalizes [Formula: text], originally proposed by Ahmed, Luedtke, SOng, Xie in 2017 , solving CCP. We first show that text] resembles bilevel optimization, where upper-level problem find objective function value enforce feasibility given from lower-level problem, minimize expectation constraint violations subject upper bound provided problem. interpretation motivates us prove when uncertain are variables, always outperforms approximation. further (i) sufficient conditions under can recover an optimal solution CCP; (ii) equivalent bilinear programming formulation inspiring enhance with convergent alternating minimization method text]); (iii) extension distributionally robust programs (DRCCPs) text]Wasserstein ambiguity set. Our numerical study demonstrates effectiveness methods. Funding: work was supported Division Civil, Mechanical Manufacturing Innovation [Grant 2046426]. Supplemental Material: The e-companion available at https://doi.org/10.1287/opre.2021.2225 .