An optimization problem on subsets of the symmetric positive-semidefinite matrices |
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Authors: | P Tarazaga M W Trosset |
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Institution: | (1) Department of Mathematics, University of Puerto Rico, Mayaguez, Puerto Rico;(2) Department of Computational and Applied Mathematics, Rice University, Houston, Texas;(3) Department of Psychology, University of Arizona, Tucson, Arizona;(4) Multidimensional Consulting, Tucson, Arizona |
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Abstract: | Motivated by the metricsstress problem in multidimensional scaling, the authors consider the more general problem of minimizing a strictly convex function on a particular subset ofR
n × n
. The subset in question is the intersection of a linear subspace with the symmetric positive-semidefinite matrices of rank p. Because of the rank restriction, this subset is not convex. Several equivalent formulations of this problem are derived, and the advantages and disadvantages of each formulation are discussed.Part of this research was conducted while the authors were visitors at the Center for Research on Parallel Computation, Rice University, Houston, Texas. The first author was partially supported by National Science Foundation Grant RII-89-05080. |
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Keywords: | Matrix optimization semidefinite constraints rank restrictions multidimensional scaling |
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