Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach

Authors:
L. Jeff Hong;Yi Yang;Liwei Zhang
Affiliations:
Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China;Department of Computer Science, University of California, Irvine, Irvine, California 92617;School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
Venue:
Operations Research
Year:
2011

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Abstract

When there is parameter uncertainty in the constraints of a convex optimization problem, it is natural to formulate the problem as a joint chance constrained program (JCCP), which requires that all constraints be satisfied simultaneously with a given large probability. In this paper, we propose to solve the JCCP by a sequence of convex approximations. We show that the solutions of the sequence of approximations converge to a Karush-Kuhn-Tucker (KKT) point of the JCCP under a certain asymptotic regime. Furthermore, we propose to use a gradient-based Monte Carlo method to solve the sequence of convex approximations.