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Tighter Reformulations using Classical Dawson and Sankoff Bounds for Approximating Two-Stage Chance-Constrained Programs

Bismark Singh (bismark.singh***at***fau.de)

Abstract: We extend and improve recent results given by Singh and Watson on using classical bounds on the union of sets in a chance-constrained optimization problem. Specifically, we improve the so-called Dawson and Sakoff bound that provided the best approximation of a chance constraint in the previous analysis. Next, we show that our work is a generalization of the previous work, and in fact the inequality employed previously is a very restrictive case that does not generally hold. Computational results demonstrate on average over a 35% improvement in the bounds.

Keywords: chance-constrained optimization ; Bonferroni inequalities ; union bounds ; stochastic optimization ; approximations

Category 1: Stochastic Programming

Category 2: Combinatorial Optimization

Citation: in review

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Entry Submitted: 08/13/2019
Entry Accepted: 08/14/2019
Entry Last Modified: 01/09/2020

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