The generalized reduced gradient method has been proven to be a precise and accurate
method for solving nonlinear programming problems. To enlarge the capability of this
method for solving wilder application problems, in this research, the concept of Conjugate
gradient and the Quasi-Newton approach are involved in the GRG algorithm whenever a
direction must be generated for its' next search. As for the determination of the step length for
each line search operation, the two phases of bracket search and square inner approximating
method are provided. A four-criteria comparison is performed, that involving the
effectiveness, efficiency, space occupation and solution precision of the three searching
directions of the GRG algorithm by testing them on a set of twenty-five testing problems.
