Parallel branch and bound for multidimensional scaling with L1 distances formulated as quadratic programming with complementarity constraints

We consider the problem of finding the global minimum of the least squares Stress function with L1 distances in multidimensional scaling. The problem can be formulated as a quadratic programming problem with complementarity constraints and solved as a two level optimization problem with combinatorial minimization at the upper level and convex quadratic programming at the lower level. In this paper, we propose a parallel branch and bound algorithm for this two level optimization problem.