A method for global minimization of nonconvex quadratic functions

Abstract

The problem of global minimization of nonconvex quadratic functions subject to box constraints is studied. Applying Gershgorin theorem we reduce the main matrix A to its diagonal form which is used to obtain difference of convex representation of the quadratic function. Then {\epsilon}-subdifferentials of DC components are studied and used to design a method for minimizing the quadratic function globally.