A New Search Direction via Hybrid Conjugate Gradient Coefficient for Solving Nonlinear System of Equations
Keywords:Unconstrained optimization; Conjugate gradient; Search direction; Nonlinear equations.
Conjugate gradient methods are widely used for unconstrained optimization problems. Most of the conjugate gradient methods do not always generate a descent search direction. In this article, a new search direction via hybrid conjugate gradient method by convex combination of the earlier works is used and extended for the solution of nonlinear system of equations. The proposed search direction generates a descent direction at every iteration and without convexity assumption on the objective function. The new method possesses, preserved and inherits the properties of the Conjugate Gradient (CG) coefficient used. The proposed hybridized method played a useful, vital and powerful role in solving large-scale nonlinear system of equations as indicated in the numerical results.
Authors publishing with MyJCAM retain the copyright of their work under the Creative Commons Attribution License (CC-BY). This license allows others to copy, distribute, display, and perform the work, provided that the original work is properly cited.
By submitting a manuscript for publication, Authors agree to the following terms.
- Authors will own the copyright to the Article.
- The manuscript submitted for publication is the author’s original work.
- Authors hereby grant to MyJCAM a free and unrestricted license to disseminate the Article electronically to anybody who asks for it.
- All authors participated in the work in a substantive way and are prepared to take public responsibility for the work.
- All authors have seen and approved the manuscript as submitted.
- The manuscript has not been published and is not being submitted or considered for publication elsewhere.
- The text, illustrations and any other materials included in the manuscript do not infringe upon any existing copyright or other rights of anyone.
- No responsibility is assumed by MyJCAM, its staff or members of the editorial board for any injury or change to person or property as a matter of product liability, negligence or otherwise of any methods, product instruction or ideas contained in this publication.