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

EURO Journal on Computational Optimization - Tập 4 - Trang 93-121 - 2015
Gabriele Eichfelder1, Tobias Gerlach1, Susanne Sumi2
1Institute for Mathematics, Technische Universität Ilmenau, Ilmenau, Germany
2Technical Mechanics Group, Technische Universität Ilmenau, Ilmenau, Germany

Tóm tắt

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.

Tài liệu tham khảo

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