Main Subjects : Optimization


A New Formula for Conjugate Gradient in Unconstrained Optimization

Hussein A. Wali; Khalil K. Abbo

AL-Rafidain Journal of Computer Sciences and Mathematics, 2020, Volume 14, Issue 1, Pages 41-52
DOI: 10.33899/csmj.2020.164798

The conjugate gradient method is an important part of the methods of optimization that are not constrained by local convergence characteristics. In this research, a new formula for the conjugated coefficient is derived depending on the linear structure. The new method fulfills the regression requirement. In addition, using the Wolff search line terms, the overall convergence of the new method has been demonstrated. At the end of the research were presented numerical results that show the effectiveness of the proposed method.
 

A Rational Triangle Function as a Model for a Conjugate Gradient Optimization Method.

Abbas Y. Al-Bayati; Basim A. Hassan

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 1, Pages 43-54
DOI: 10.33899/csmj.2006.164034

This paper presents the development and implementation of a new numberical based on a non-quadratic Triangular rational function model. For solving non-linear optimization problem .The algorithm is implemented in one version, employing exact line search. This version is compared numberically against versions of the CG-method. The results indicate that in general the new algorithm is superior to the previon algorithm.
 

New Initial Parameter for the Constrained Optimization Method

Abbas Y. Al-Bayati; Ban Ahmed Mitras

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 1, Pages 61-68
DOI: 10.33899/csmj.2006.164036

In this paper, we have investigated a new initial parameter in the nonlinear constrained optimization method. The aim of this new method is to make a balance between interior and exterior method for constrained optimization. The new technique has been programmed to solve some of standard problems in the non-linear optimization. The results are too effective when compared with other standard optimization methods like interior and exterior methods.
 

In Accurate CG-Algorithm for Unconstrained Optimization Problems

Nidhal Al-Assady; Maysoon M. Aziz; Ban Ahmed Mitras

AL-Rafidain Journal of Computer Sciences and Mathematics, 2004, Volume 1, Issue 1, Pages 34-53
DOI: 10.33899/csmj.2004.164096

An algorithm for unconstrained minimization is proposed which is invariant to a non-linear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic function. It is derived for inexact line searches and is designed for general use, it compares favorably numerical tests [over eight test functions and dimensionally up to (2-100) with the H/S, DX, F/R, P/R, and A/B algorithms on which this new algorithm is based.