Using a New Nonlinear Gradient Method for Solving Large Scale Convex Optimization Problems with an Application on Arabic Medical Text

TL;DR

This paper introduces a novel nonlinear gradient method that hybridizes two conjugate coefficients to efficiently solve large-scale convex optimization problems, demonstrating its effectiveness on standard benchmarks and an Arabic medical text application.

Contribution

A new nonlinear gradient method combining HRM and NHS coefficients for improved convex optimization, with demonstrated stability and efficiency in practical applications.

Findings

Successfully solved standard convex problems with exact solutions for quadratic cases.

Proved the method's stability and efficiency in Arabic medical text entity recognition.

Achieved faster execution times compared to existing methods.

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 [2] and NHS [1]. 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.