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Convergence Analysis and a DC Approximation Method for Data-driven Mathematical Programs with Distributionally Robust Chance Constraints

Sun Hailin(hlsun***at***njnu.edu.cn)
Zhang Dali(zhangdl***at***sjtu.edu.cn)
Chen Yannan(ynchen***at***scnu.edu.cn)

Abstract: In this paper, we consider the convergence analysis of data-driven mathematical programs with distributionally robust chance constraints (MPDRCC) under weaker conditions without continuity assumption of distributionally robust probability functions. Moreover, combining with the data-driven approximation, we propose a DC approximation method to MPDRCC without some special tractable structures. We also give the convergence analysis of the DC approximation method without continuity assumption of distributionally robust probability functions and apply a recent DC algorithm to solve them. The numerical tests verify the theoretical results and show the effectiveness of the data-driven approximated DC approximation method.

Keywords: Distributionally robust optimization, chance constraints, data-driven, convergence analysis, DC approximation

Category 1: Robust Optimization

Category 2: Stochastic Programming


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Entry Submitted: 11/07/2019
Entry Accepted: 11/07/2019
Entry Last Modified: 11/07/2019

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