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Adaptive Robust Optimization with Scenario-wise Ambiguity Sets

Zhi Chen (chenzhi.james***at***gmail.com)
Melvyn Sim (melvynsim***at***gmail.com)
Peng Xiong (xiongpengnus***at***gmail.com)

Abstract: We present a tractable format for optimization under uncertainty based on the framework of adaptive robust optimization via a new class of scenario-wise ambiguity sets. The new format naturally unifies classical stochastic programming and robust optimization, and also incorporates the more recent distributionally robust optimization with ambiguity sets based on generalized moments, mixture distribution, Wasserstein (or Kantorovich-Rubinstein) metric, phi-divergence, and new ones such as k-means clustering, among others. We introduce a compatible scenario-wise affine recourse approximation, which is developed on the classical affine recourse approximation (a.k.a. linear decision rule or affine policy), to provide tractable solutions to adaptive robust optimization problems. To illustrate the modeling power of this new format, we develop a new algebraic modeling package, AROMA and demonstrate how it can be used to deliver tractable solutions to adaptive robust optimization problems.

Keywords: distributionally robust optimization, adaptive robust optimization, Wasserstein metric, phi-divergence, k-means, mixture distribution

Category 1: Robust Optimization

Category 2: Stochastic Programming

Citation: NUS Business School working paper

Download: [PDF]

Entry Submitted: 06/02/2017
Entry Accepted: 06/02/2017
Entry Last Modified: 05/30/2018

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