Simplicial Global Optimization

  • Remigijus Paulavičius
  • Julius Žilinskas

Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-x
  2. Remigijus Paulavičius, Julius Žilinskas
    Pages 1-19
  3. Remigijus Paulavičius, Julius Žilinskas
    Pages 21-60
  4. Remigijus Paulavičius, Julius Žilinskas
    Pages 61-86
  5. Remigijus Paulavičius, Julius Žilinskas
    Pages 87-106
  6. Back Matter
    Pages 107-137

About this book

Introduction

Simplicial Global Optimization is centered on deterministic covering methods partitioning feasible region by simplices. This book looks into the advantages of simplicial partitioning in global optimization through applications where the search space may be significantly reduced while taking into account symmetries of the objective function by setting linear inequality constraints that are managed by initial partitioning. The authors provide an extensive experimental investigation and illustrates the impact of various bounds, types of subdivision, strategies of candidate selection on the performance of algorithms. A comparison of various Lipschitz bounds over simplices and an extension of Lipschitz global optimization with-out the Lipschitz constant to the case of simplicial partitioning is also depicted in this text. Applications benefiting from simplicial partitioning are examined in detail such as nonlinear least squares regression and pile placement optimization in grillage-type foundations. Researchers and engineers will benefit from simplicial partitioning algorithms such as Lipschitz branch and bound, Lipschitz optimization without the Lipschitz constant, heuristic partitioning presented. This book will leave readers inspired to develop simplicial versions of other algorithms for global optimization and even use other non-rectangular partitions for special applications.

Keywords

Lipschitz optimization Simplicial partitions branch and bound heuristic partitioning nonlinear least squares regression potentially optimal simplex

Authors and affiliations

  • Remigijus Paulavičius
    • 1
  • Julius Žilinskas
    • 2
  1. 1.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-9093-7
  • Copyright Information Remigijus Paulavičius, Julius Žilinskas 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-9092-0
  • Online ISBN 978-1-4614-9093-7
  • Series Print ISSN 2190-8354
  • Series Online ISSN 2191-575X
  • About this book