Abstract: Gradient methods have applications in multiple fields, including signal
processing, image processing, and dynamic systems. In this paper, we present a
nonlinear gradient method for solving convex supra-quadratic functions by
developing the search direction, that done by hybridizing between the two
conjugate coefficients HRM  and NHS . The numerical results proved the
effectiveness of the presented method by applying it to solve standard problems
and reaching the exact solution if the objective function is quadratic convex.
Also presented in this article, an application to the problem of named entities
in the Arabic medical language, as it proved the stability of the proposed
method and its efficiency in terms of execution time.