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Derivative-free optimization methods

Published online by Cambridge University Press:  14 June 2019

Jeffrey Larson ,
Matt Menickelly  and
Stefan M. Wild
Jeffrey Larson
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL 60439, USA E-mail: [email protected], [email protected], [email protected]
Matt Menickelly
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL 60439, USA E-mail: [email protected], [email protected], [email protected]
Stefan M. Wild
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL 60439, USA E-mail: [email protected], [email protected], [email protected]
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Abstract

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

Type
Research Article
Information
Acta Numerica , Volume 28 , 01 May 2019 , pp. 287 - 404
Copyright
© Cambridge University Press, 2019 

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