Global Optimality Conditions Of Quadratically Constrained Quadratic Programming Problems

Quadratically constrained quadratic programming problems are worthy of study both because they frequently appear in many applied field of science and technology, and many other nonlinear problems are converted into this form. This paper present a new approach which make use of a global subdifferential: L- subdifferentail. Unlike local or convex subdifferential,an L-subdifferential is defined by functions which are not necessarily linear functions. We consided global optimality conditions of some quadratically constrained quadratic programming problems.In the first chapter of this paper, we first introduce the recent developments in global optimality conditions, then we introduce the definitions of L-subdifferential and L-normal cone. Finally, we obtain some global optimality conditions for non-convex quadratic minimization problems with quadratic constraints. The global optimality conditions of 0-1 programming problems are discussed in chaper two. In chaper three,we establish conditions which endure that a feasible point is a global minimization problem subject to box constraints and quadratic intger minimization problem subject to box constraints. In chaper four, we consider the constrained optimization problem with a quadratic cost functional and two quadratic equality constraints. A necessary and sufficient condition to characterize a local optimal solution to be global is established.