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Bounds for Probabilistic Constrained Problems

Shen Peng(Shen.Peng***at***lri.fr)
Abdel Lisser(Abdel.Lisser***at***lri.fr)
Francesca Maggioni(francesca.maggioni***at***unibg.it)

Abstract: In this paper we develop four upper bounds for single and joint chance constraints with independent matrix vector rows. The deterministic approximations of the probability constraints are based on the one-side Chebyshev inequality, Chernoff inequality, Bernstein in- equality and Hoeffding inequality. Various sufficient conditions under which the aforementioned approximations are convex and tractable are derived. Therefore, we reformulate the chance constrained problems as tractable convex optimization problems based on piecewise linear and tangent approximations allowing to reduce further the computational complexity. Finally, numerical results on randomly generated data are discussed allowing to identify the tighter deterministic approximations.

Keywords: stochastic programming, chance-constrained problem, bounds, single chance-constraint, joint chance-constraints, piecewise approximations

Category 1: Stochastic Programming

Citation: Submitted to Journal of Optimization Theory and Applications on October 16 2018

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Entry Submitted: 10/24/2018
Entry Accepted: 10/24/2018
Entry Last Modified: 10/24/2018

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