Abstract
In this paper we develop convex relaxations of chance constrained optimization problems in order to obtain lower bounds on the optimal value. Unlike existing statistical lower bounding techniques, our approach is designed to provide deterministic lower bounds. We show that a version of the proposed scheme leads to a tractable convex relaxation when the chance constraint function is affine with respect to the underlying random vector and the random vector has independent components. We also propose an iterative improvement scheme for refining the bounds.
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Acknowledgments
The improvement scheme of Sect. 4 was inspired by on-going joint research with Santanu S. Dey, Feng Qiu and Laurence Wolsey on a coefficient tightening scheme for integer programming formulations of chance constrained linear programs under discrete distributions. The author thanks Arkadi Nemirovski for some helpful comments. This work was supported in part by AFOSR Grant FA9550-12-1-0154 and NSF Grant CMMI-1129871.
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Ahmed, S. Convex relaxations of chance constrained optimization problems. Optim Lett 8, 1–12 (2014). https://doi.org/10.1007/s11590-013-0624-7
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DOI: https://doi.org/10.1007/s11590-013-0624-7