Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach
L. Jeff Hong, Yi Yang, Liwei Zhang
Operations Research · 2011 · Volume 59 · Issue 3
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.
Keywords
programming, stochastic, chance constrained program
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