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Applications of Global Optimization Benefiting from Simplicial Partitions

  • Remigijus Paulavičius
  • Julius Žilinskas
Chapter
Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

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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Copyright information

© Remigijus Paulavičius, Julius Žilinskas 2014

Authors and Affiliations

  • Remigijus Paulavičius
    • 1
  • Julius Žilinskas
    • 1
  1. 1.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania

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