Derivative-free robust optimization by outer approximations

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the a...

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Vydané v:	Mathematical programming Ročník 179; číslo 1-2; s. 157 - 193
Hlavní autori:	Menickelly, Matt, Wild, Stefan M.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020 Springer Nature B.V Springer
Predmet:	Algorithms Approximation BASIC BIOLOGICAL SCIENCES Calculus of Variations and Optimal Control; Optimization Combinatorics Derivative-free optimization Full Length Paper Manifold sampling Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Minimax technique Nonlinear programming Numerical Analysis Optimization Outer approximation algorithms Robust optimization Robustness Theoretical Robust optimization 90C30 Outer approximation algorithms 90C47 Manifold sampling 90C56 65K10 Derivative-free optimization
ISSN:	0025-5610, 1436-4646
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Abstract	We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.
AbstractList	We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.
Author	Menickelly, Matt Wild, Stefan M.
Author_xml	– sequence: 1 givenname: Matt orcidid: 0000-0002-2023-0837 surname: Menickelly fullname: Menickelly, Matt email: mmenickelly@anl.gov organization: Mathematics and Computer Science Division, Argonne National Laboratory – sequence: 2 givenname: Stefan M. surname: Wild fullname: Wild, Stefan M. organization: Mathematics and Computer Science Division, Argonne National Laboratory
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Copyright	UChicago Argonne, LLC, Operator of Argonne National Laboratory 2018 Mathematical Programming is a copyright of Springer, (2018). All Rights Reserved. 2018© UChicago Argonne, LLC, Operator of Argonne National Laboratory 2018
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Snippet	We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an...
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SubjectTerms	Algorithms Approximation BASIC BIOLOGICAL SCIENCES Calculus of Variations and Optimal Control; Optimization Combinatorics Derivative-free optimization Full Length Paper Manifold sampling Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Minimax technique Nonlinear programming Numerical Analysis Optimization Outer approximation algorithms Robust optimization Robustness Theoretical
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Title	Derivative-free robust optimization by outer approximations
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