A Method for Solving the Indefinite Quadratic Programming Problem

A method is developed for obtaining a solution to the quadratic programming problem with an indefinite quadratic objective function. A search procedure using gradient projection is the core of the method. However at each step an alternate direction to gradient projection is proposed and two methods are given to continue after the revised gradient projection procedure terminates. Although convergence to the solution is not guaranteed, good results were obtained for fifty-seven problems used to test the method.