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Branch and bound algorithm for multidimensional scaling with city-block metric. (English) Zbl 1179.90250
Summary: A two level global optimization algorithm for multidimensional scaling (MDS) with city-block metric is proposed. The piecewise quadratic structure of the objective function is employed. At the upper level a combinatorial global optimization problem is solved by means of branch and bound method, where an objective function is defined as the minimum of a quadratic programming problem. The later is solved at the lower level by a standard quadratic programming algorithm. The proposed algorithm has been applied for auxiliary and practical problems whose global optimization counterpart was of dimensionality up to 24.

MSC:
90C20 Quadratic programming
90C27 Combinatorial optimization
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