Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/136363
Title: DISTRIBUTIONALLY ROBUST OPTIMIZATION WITH INFINITELY CONSTRAINED AMBIGUITY SETS
Authors: CHEN ZHI
Keywords: Distributionally robust optimization, ambiguity set, data-driven optimization, decision making under uncertainty, Wasserstein distance
Issue Date: 9-May-2017
Citation: CHEN ZHI (2017-05-09). DISTRIBUTIONALLY ROBUST OPTIMIZATION WITH INFINITELY CONSTRAINED AMBIGUITY SETS. ScholarBank@NUS Repository.
Abstract: In this thesis, we motivate and introduce the class of infinitely constrained ambiguity sets. We demonstrate how an infinitely constrained ambiguity set, with infinitely many expectation constraints, is enriched in characterizing uncertainty in its description. We study both static and adaptive distributionally robust optimization models with infinitely constrained ambiguity sets. We propose a tractable solution procedure to obtain approximate solutions, which can be iteratively refined. We present a unified and tractable framework for distributionally robust optimization with data that could encompass a variety of statistical information including, among other things, constraints on expectation, conditional expectation, disjoint confidence sets with uncertain probabilities defined by phi-divergence, and proximity to the reference distribution measured by the Wasserstein distance. To address a distributionally robust optimization problem with recourse, we introduce the tractable adaptive recourse scheme, which is based on the classical linear decision rule and can be applied in situations involving discrete recourse decisions.
URI: http://scholarbank.nus.edu.sg/handle/10635/136363
Appears in Collections:Ph.D Theses (Open)

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