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Parallel branch and bound for multidimensional scaling with city-block distances. (English) Zbl 1259.90126

Summary: Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is the minimization of a multimodal function with unfavorable properties like invariants and nondifferentiability. Recently, a branch-and-bound algorithm for multidimensional scaling with city-block distances has been proposed for solution of medium-size problems exactly. The algorithm exploits piecewise quadratic structure of the objective function. In this paper, a parallel version of the branch-and-bound algorithm for multidimensional scaling with city-block distances is and investigated. Parallel computing enabled solution of larger problems which is not feasible with the sequential version.

MSC:

90C30 Nonlinear programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut

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