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Erschienen in:
Introduction: Tools and Challenges in Derivative-Free and Blackbox Optimization Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

8. Mesh Adaptive Direct Search

verfasst von : Charles Audet, Warren Hare

Erschienen in: Derivative-Free and Blackbox Optimization

Verlag: Springer International Publishing

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Abstract

Chapter 3 proposed the coordinate search (CS) algorithm for unconstrained optimization. The algorithm worked based on local exploration around the incumbent solution in the positive and negative orthogonal coordinate directions. In Chapter 7, this algorithm was expanded to allow a broader use of search directions, resulting in the generalised pattern search (GPS) algorithm. However, the convergence analysis of the GPS algorithm falls a little short of what we would like. First, the main result states that if the objective function f is locally Lipschitz, then the generalised directional derivatives are nonnegative for only a finite set of directions. Second, and more importantly, the analysis only examined unconstrained optimization problems. In practice, there are very few problems in which the variables are free to take any values.

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Vorheriges Kapitel Generalised Pattern Search
Nächstes Kapitel Building Linear and Quadratic Models
Fußnoten
1
An orthonormal basis is composed of orthogonal and unit vectors.
 
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Metadaten
Titel
Mesh Adaptive Direct Search
verfasst von
Charles Audet
Warren Hare
Copyright-Jahr
2017
Buch
Derivative-Free and Blackbox Optimization

Print ISBN: 978-3-319-68912-8

Electronic ISBN: 978-3-319-68913-5

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-68913-5_8

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