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Tractable Format for Distributionally Robust Optimization

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Tractable Format for Distributionally Robust Optimization
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39
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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We present a unified and tractable framework for distributionally robust optimization that could encompass a variety of statistical information including, among others things, constraints on expectation, scenario-wise expectations, Wasserstein metric, and uncertain probabilities defined by phi-divergence. To address a distributionally robust optimization problem with recourse, we introduce the scenario wise linear decision rule, which is based on the classical linear decision rule and can also be applied in situations where the recourse decisions are discrete. Based in this format, we has also developed a new Matlab based algebraic modeling language to model and solve distributionally robust optimization problems with recourse.