A modification of the alphaBB method for box-constrained optimization and an application to inverse kinematics

Eichfelder, Gabriele GND; Gerlach, Tobias GND; Sumi, Susanne

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. For determining a representation of the global optimal solution set with a predefined quality we modify the well known BB method. We illustrate the properties and give a proof for the finiteness and correctness of our modified BB method.

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Eichfelder, Gabriele / Gerlach, Tobias / Sumi, Susanne: A modification of the alphaBB method for box-constrained optimization and an application to inverse kinematics. 2015.

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