Extreme point quadratic minimization problem

In the present paper a non-convex quadratic programming problem is studied in which the optimal feasible solution in addition to satisfying a general set of constraints is required to be an extreme point of a convex polytope. A linear programming problem is constructed whose basic feasible solutions are ranked in non-decreasing order of the value of its objective function and this in turn ranks the extreme points of the convex polytope in non-decreasing order of the value of the objective function of the aforementioned quadratic programming problem. The ranking of extreme points is carried out till an optimal feasible solution of the main problem is obtained.