Robust optimization methods for chance constrained, simulation-based, and bilevel problems

I. Yanikoglu

Research output: ThesisDoctoral ThesisScientific

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Abstract

The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Tilburg University
Supervisors/Advisors
  • den Hertog, Dick, Promotor
  • Kuhn, D., Co-promotor, External person
Award date2 Sep 2014
Place of PublicationTilburg
Publisher
Print ISBNs9789056683924
Publication statusPublished - 2 Sep 2014

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Robust Optimization
Robust Methods
Optimization Methods
Optimization Problem
Simulation
Uncertainty
Bilevel Optimization
Simulation-based Optimization
Tractability
Uncertain Parameters
Historical Data
Stochastic Optimization
Optimization Techniques
Methodology
Approximation
Range of data
Class

Cite this

Yanikoglu, I. (2014). Robust optimization methods for chance constrained, simulation-based, and bilevel problems. Tilburg: CentER, Center for Economic Research.
Yanikoglu, I.. / Robust optimization methods for chance constrained, simulation-based, and bilevel problems. Tilburg : CentER, Center for Economic Research, 2014. 161 p.
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abstract = "The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques.",
author = "I. Yanikoglu",
year = "2014",
month = "9",
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Yanikoglu, I 2014, 'Robust optimization methods for chance constrained, simulation-based, and bilevel problems', Doctor of Philosophy, Tilburg University, Tilburg.

Robust optimization methods for chance constrained, simulation-based, and bilevel problems. / Yanikoglu, I.

Tilburg : CentER, Center for Economic Research, 2014. 161 p.

Research output: ThesisDoctoral ThesisScientific

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AU - Yanikoglu, I.

PY - 2014/9/2

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N2 - The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques.

AB - The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques.

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Yanikoglu I. Robust optimization methods for chance constrained, simulation-based, and bilevel problems. Tilburg: CentER, Center for Economic Research, 2014. 161 p. (CentER Dissertation Series).