Primal and polar approach for computing the symmetric diagonally dominant projection

We solve the problem of minimizing the distance from a given matrix to the cone of symmetric and diagonally dominant matrices with positive diagonal (SDD⁺). Using the extreme rays of the polar cone we project onto the supporting hyperplanes of the faces of SDD⁺ and then, applying the cyclic Dykstra's algorithm, we solve the problem. Similarly, using the extreme rays of SDD⁺ we characterize the projection onto the polar cone, which also allows us to obtain the projection onto SDD⁺ by means of the orthogonal decomposition theorem for convex cones. In both cases the symmetry and the sparsity pattern of the given matrix are preserved. Preliminary numerical experiments indicate that the polar approach is a promising one. Copyright © 2002 John Wiley & Sons, Ltd.