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Data-Driven Chance Constrained Optimization


B. Stellato

Master-Thesis, FS14 (10329)

Traditional optimization methods for decison-making under uncertainty assume perfect model information. In practice, however, such precise knowledge is rarely available. Thus, optimal decisions coming from these approaches can be very sensitive to perturbations and unreliable. Stochastic optimization programs take into account uncertainty but are intractable in general and need to be approximated. Of late, distributionally robust optimization methods have shown to be powerful tools to reformulate stochastic programs in a tractable way. Moreover, the recent advent of cheap sensing devices has caused the explosion of available historical data, usually referred to as \Big Data". Thus, modern optimization techniques are shifting from traditional methods to data-driven approaches. In this thesis, we derive data-driven tractable reformulations for stochastic optimization programs based on distributionally robust optimization. In the rst part of this work we provide our theo- retical contributions. New distributionally robust probability bounds are derived and used to re- formulate uncertain optimization programs assuming limited information about the uncertainty. Then, we show how this information can be derived from historical data. In the second part of this work, we compare the developed methods to support vector machines in a machine learning setting and to randomized optimization and in a control context.


Type of Publication:

(12)Diploma/Master Thesis

B. P. Van Parys

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2014:IFA_4972
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