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Chance Constrained Programs with Mixture Distributions

Zhaolin Hu (russell***at***tongji.edu.cn)
Wenjie Sun (r13381638770***at***sina.com)
Shushang Zhu (zhuss***at***mail.sysu.edu.cn)

Abstract: Chance constrained programs (CCP) are important models in stochastic optimization. In the main conventional literature on CCPs, the underlying distribution that models the randomness of the problem is usually assumed to be given in advance. However, in practice, such a distribution needs to be specified by the modelers based on the data/information available. This is called input modeling. In this paper we consider input modeling in CCPs. We propose to use mixture distributions to fit the data available and to model the randomness. We demonstrate the merits of using mixture distributions and show how to handle the CCPs with mixture distributions. Furthermore, we consider several scenarios that arise from practical applications and analyze how the problem structures could embrace alternative optimization techniques. We also conduct numerical experiments to demonstrate our approach.

Keywords: Chance Constrained Program, Gaussian Mixture Model, Gradient Estimation, Branch-and-Bound Algorithm

Category 1: Stochastic Programming

Category 2: Nonlinear Optimization


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Entry Submitted: 09/01/2018
Entry Accepted: 09/01/2018
Entry Last Modified: 10/30/2018

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