On the steepest descent algorithm for quadratic functions

The steepest descent algorithm with exact line searches (Cauchy algorithm) is inefficient, generating oscillating step lengths and a sequence of points converging to the span of the eigenvectors associated with the extreme eigenvalues. The performance becomes very good if a short step is taken at every (say) 10 iterations. We show a new method for … Read more

On cones of nonnegative quadratic functions

We derive LMI-characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co-positivity. These matrix cones are in fact cones of non-convex quadratic functions that are nonnegative on a certain domain. As a domain, we consider for instance the intersection of a (upper) level-set of a quadratic … Read more