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EURO Journal on Computational Optimization

, Volume 4, Issue 1, pp 93–121 | Cite as

A modification of the \(\alpha \hbox {BB}\) method for box-constrained optimization and an application to inverse kinematics

  • Gabriele EichfelderEmail author
  • Tobias Gerlach
  • Susanne Sumi
Original Paper

Abstract

For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information which cannot be formulated as a mathematical function or within a hierarchical problem formulation. We present such an application in the field of robotic design. This application problem can be modeled as a smooth box-constrained optimization problem. We extend the well-known \(\alpha \hbox {BB}\) method such that it can be used to find an approximation of the set of globally optimal solutions with a predefined quality. We illustrate the properties and give a proof for the finiteness and correctness of our modified \(\alpha \hbox {BB}\) method.

Keywords

Non-convex programming Global optimization Optimal solution set \(\alpha \hbox {BB}\) method Robotic design 

Mathematics Subject Classification

90C26 90C30 90C90 

Notes

Acknowledgments

The authors thank the two anonymous referees for their careful reading and their helpful comments on the first version of this manuscript.

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Copyright information

© EURO - The Association of European Operational Research Societies 2015

Authors and Affiliations

  • Gabriele Eichfelder
    • 1
    Email author
  • Tobias Gerlach
    • 1
  • Susanne Sumi
    • 2
  1. 1.Institute for MathematicsTechnische Universität IlmenauIlmenauGermany
  2. 2.Technical Mechanics GroupTechnische Universität IlmenauIlmenauGermany

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