Aspects of quadratic optimization - nonconvexity, uncertainty, and applications

Ahmadreza Marandi

Research output: ThesisDoctoral ThesisScientific

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Abstract

Quadratic Optimization (QO) has been studied extensively in the literature due to its application in real-life problems. This thesis deals with two complicated aspects of QO problems, namely nonconvexity and uncertainty. A nonconvex QO problem is intractable in general. The first part of this thesis presents methods to approximate a nonconvex QP problem. Another important aspect of a QO problem is taking into account uncertainties in the parameters since they are mostly approximated/estimated from data. The second part of the thesis contains analyses of two methods that deal with uncertainties in a convex QO problem, namely Static and Adjustable Robust Optimization problems. To test the methods proposed in this thesis, the following three real-life applications have been considered: pooling problem, portfolio problem, and norm approximation problem.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Tilburg University
Supervisors/Advisors
  • de Klerk, Etienne, Promotor
  • den Hertog, Dick, Promotor
Award date11 Dec 2017
Place of PublicationTilburg
Publisher
Print ISBNs978 90 5668 534 8
Publication statusPublished - 2017

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Non-convexity
Quadratic Optimization
Optimization Problem
Uncertainty
Nonconvex Optimization
Robust Optimization
Pooling
Approximation Problem
Convex Optimization
Norm

Cite this

Marandi, A. (2017). Aspects of quadratic optimization - nonconvexity, uncertainty, and applications. Tilburg: CentER, Center for Economic Research.
Marandi, Ahmadreza. / Aspects of quadratic optimization - nonconvexity, uncertainty, and applications. Tilburg : CentER, Center for Economic Research, 2017. 164 p.
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Marandi, A 2017, 'Aspects of quadratic optimization - nonconvexity, uncertainty, and applications', Doctor of Philosophy, Tilburg University, Tilburg.

Aspects of quadratic optimization - nonconvexity, uncertainty, and applications. / Marandi, Ahmadreza.

Tilburg : CentER, Center for Economic Research, 2017. 164 p.

Research output: ThesisDoctoral ThesisScientific

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AU - Marandi, Ahmadreza

PY - 2017

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N2 - Quadratic Optimization (QO) has been studied extensively in the literature due to its application in real-life problems. This thesis deals with two complicated aspects of QO problems, namely nonconvexity and uncertainty. A nonconvex QO problem is intractable in general. The first part of this thesis presents methods to approximate a nonconvex QP problem. Another important aspect of a QO problem is taking into account uncertainties in the parameters since they are mostly approximated/estimated from data. The second part of the thesis contains analyses of two methods that deal with uncertainties in a convex QO problem, namely Static and Adjustable Robust Optimization problems. To test the methods proposed in this thesis, the following three real-life applications have been considered: pooling problem, portfolio problem, and norm approximation problem.

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M3 - Doctoral Thesis

SN - 978 90 5668 534 8

T3 - CentER Dissertation Series

PB - CentER, Center for Economic Research

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Marandi A. Aspects of quadratic optimization - nonconvexity, uncertainty, and applications. Tilburg: CentER, Center for Economic Research, 2017. 164 p. (CentER Dissertation Series).