QUADRATIC FORMS SEMI-DEFINITE OVER CONVEX CONES
Richard W. Cottle, George J. Habetler, C. E. Lemke · Princeton University Press eBooks · 2015
Abstract : A differentiable function on a convex set K is said to be K-flat if its gradient vanishes at each of its zeros belonging to K. K-flatness of quadratic forms implies their constrained semi-definiteness. This furnishes a useful characterization of positive semi-definite matrices (when K is the whole space) and 'copositive-plus' matrices (when K is the non-negative orthant). Parallel comparisions between these classes of matrices are made. (Author)