Accession Number : AD0702870

Title :   QUADRATIC FORMS SEMI-DEFINITE OVER CONVEX CONES.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF OPERATIONS RESEARCH HOUSE

Personal Author(s) : Cottle,Richard W. ; Habetler,G. J. ; Lemke,C. E.

Report Date : 18 AUG 1967

Pagination or Media Count : 28

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)

Descriptors :   (*MATHEMATICAL PROGRAMMING, MATRICES(MATHEMATICS)), CONVEX SETS, INEQUALITIES, THEOREMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE