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

Gabriele Eichfelder (), Tobias Gerlach () and Susanne Sumi ()
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Gabriele Eichfelder: Technische Universität Ilmenau
Tobias Gerlach: Technische Universität Ilmenau
Susanne Sumi: Technische Universität Ilmenau

EURO Journal on Computational Optimization, 2016, vol. 4, issue 1, No 6, 93-121

Abstract: 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 $$\alpha \hbox {BB}$$ α 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 $$\alpha \hbox {BB}$$ α BB method.

Keywords: Non-convex programming; Global optimization; Optimal solution set; $$\alpha \hbox {BB}$$ α BB method; Robotic design; 90C26; 90C30; 90C90 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13675-015-0056-5

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