An optimization problem on subsets of the symmetric positive-semidefinite matrices

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.