Keywords : conjugate gradient method

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 Globally Convergence Spectral Conjugate Gradient Method for Solving Unconstrained Optimization Problems

Basim A. Hassan

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 4, Pages 21-28
DOI: 10.33899/csmj.2013.163543

In this paper, a modified spectral conjugate gradient method for solving unconstrained optimization problems is studied, which has sufficient descent direction and global convergence with an inexact line searches. The Fletcher-Reeves restarting criterion was employed to the standard and new versions and gave dramatic savings in the computational time. The Numerical results show that the proposed method is effective by comparing it with the FR-method.

New Conjugacy Coefficient for Conjugate Gradient Method for Unconstrained Optimization

Hamsa TH. Chilmeran; Huda Y. Najm

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 2, Pages 33-46
DOI: 10.33899/csmj.2013.163473

In this paper, we derived a new conjugacy coefficient of conjugate gradient method which is based on non-linear function using inexact line searches. This method satisfied sufficient descent condition and the converges globally is provided. The numerical results indicate that the new approach yields very effective depending on number of iterations and number of functions evaluation .

Three Proposed Hybrid Genetic Algorithms

Ban A. Mitras; Nada F. Hassan

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 1, Pages 53-64
DOI: 10.33899/csmj.2013.163424

Genetic Algorithm has been hybridized with classical optimization methods. Hybridization has been done in three approaches, by using conjugate gradient algorithm for Fletcher and Reeves, second by using steepest descent method and lastly by creation of initial population for genetic algorithm from one of conjugate gradient method, the numerical results were encouraging.

On New Conjugate Pair Method

Abbas Y. Al-Bayati; Nidhal Al-Assady; Ban Ahmed Mitras

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 2, Pages 21-29
DOI: 10.33899/csmj.2009.163793

This paper involves the combination between the conjugate pair and hybrid conjugate gradient methods. The new combined algorithm is based on exact line search and it is examined by using different nonlinear test functions in various dimensions.  Experimental results indicate that the updated algorithm is more effective than of the two original algorithms.

Investigated Non-Conic Model for Constrained Optimization

Eman Tarik Al-Haj Saeed; Huda Issam Ahmed

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 173-182
DOI: 10.33899/csmj.2008.163980

In this search,  we develop the nonlinear constrained optimization by investigation a new region of solution depending on extended conic model to non-conic model by using conjugate gradient method. The new method is too effective when compared with other established algorithms to solve standard constrained optimization problems it performance from evaluations were the number of function (NOF),number of iteration (NOI) and  the number of constrained (NOC).