AN OPTIMIZATION PROBLEM ON SUBSETS OF THE SYMMETRICAL POSITIVE-SEMIDEFINITE MATRICES

Motivated by the metric SSTRESS problem in multidimensional scaling, t he authors consider the more general problem of minimizing a strictly convex function on a particular subset of R(nxn). The subset in questi on is the intersection of a linear subspace with the symmetric positiv e-semidefinite matrices of rank less-than-or-equal-to p. Because of th e rank restriction, this subset is not convex. Several equivalent form ulations of this problem are derived, and the advantages and disadvant ages of each formulation are discussed.