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Published in:
Simplicial Partitions in Global Optimization Read chapter Read first chapter

2014 | OriginalPaper | Chapter

4. Applications of Global Optimization Benefiting from Simplicial Partitions

Authors : Remigijus Paulavičius, Julius Žilinskas

Published in: Simplicial Global Optimization

Publisher: Springer New York

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Abstract

In this chapter we discuss global optimization problems where simplicial partitioning is preferable. Most of the applications discussed here involve global optimization problems with a symmetric objective functions. As it was discussed in Sect. 1.​4 the feasible region may be reduced by setting linear constraints in order to avoid equivalent subregions due to the symmetry in the objective function. The resulting constrained feasible region can be covered by simplices and in the case the objective function is invariant to exchange of all variables and the original feasible region is a hyper-cube, the resulting constrained feasible region is a simplex. Therefore such a simplex may be used as a feasible region reducing the hyper-volume by a factor n! times and the numbers of minimizers similarly.

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previous chapter Simplicial Lipschitz Optimization Without Lipschitz Constant
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Metadata
Title
Applications of Global Optimization Benefiting from Simplicial Partitions
Authors
Remigijus Paulavičius
Julius Žilinskas
Copyright Year
2014
Publisher
Springer New York
Book
Simplicial Global Optimization

Print ISBN: 978-1-4614-9092-0

Electronic ISBN: 978-1-4614-9093-7

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4614-9093-7_4