Keywords : Conjugate Gradient


New Scaled Proposed formulas For Conjugate Gradient Methods in Unconstrained Optimization

Abbas Y. Al-Bayati; Marwan S. Jameel

AL-Rafidain Journal of Computer Sciences and Mathematics, 2014, Volume 11, Issue 2, Pages 25-46
DOI: 10.33899/csmj.2014.163748

In this paper, three efficient Scaled Nonlinear Conjugate Gradient (CG) methods for solving unconstrained optimization problems are proposed. These algorithms are implemented with inexact line searches (ILS). Powell restarting criterion is applied to all these algorithms and gives dramatic saving in the computational efficiency. The global convergence results of these algorithms are established under the Strong Wolfe line search condition. Numerical results show that our proposed CG-algorithms are efficient and stationary by comparing with standard Fletcher-Reeves (FR); Polak-Ribiere (PR) CG-algorithms, using 35-nonlinear test functions.
 

A Modified Class of Conjugate Gradient Algorithms Based on Quadratic Model for Nonlinear Unconstrained Optimization

Basim A. Hassan; Hameed M. Sadiq

AL-Rafidain Journal of Computer Sciences and Mathematics, 2014, Volume 11, Issue 1, Pages 25-37
DOI: 10.33899/csmj.2014.163729

In this paper, we have investigated a new class of conjugate gradient algorithms for unconstrained non-linear optimization which are based on the quadratic model. Some theoretical results are investigated which are sufficient descent and ensure the local convergence of the new proposed algorithms. Numerical results show that the proposed algorithms are effective by comparing with the Polak and Ribiere algorithm.
 
 

New Scale Dai-Yaun Conjugate Gradient Method for Unconstrained Optimization

Hamsa Th. Chilmerane

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 4, Pages 29-41
DOI: 10.33899/csmj.2013.163544

Conjugate gradient algorithm is widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we suggest a modified Dai-Yuan conjucay coefficient of conjugate gradient algorithm and propose new spectral form three-term conjugate gradient algorithm. These algorithms are used inexact line searches and Wolf line search conditions. These algorithms satisfied sufficient descent condition and the converge globally are provided under some assumptions. The numerical results indicate that the proposed algorithm is very effective and the new spectral algorithm is of very robust results depending on iterations and the number of known functions.
 

Modified the CG-Algorithm for Unconstrained Non-Linear Optimization by Using Oren’s Update

Abbas Y. Al-Bayati; Abdulghafor M. Al-Rozbayani

AL-Rafidain Journal of Computer Sciences and Mathematics, 2005, Volume 2, Issue 2, Pages 11-19
DOI: 10.33899/csmj.2005.164078

In this paper we have modified a new extended generalized conjugate gradient steps with self-scaling variable metric updates for unconstrained optimization. The new proposed algorithm is based on the inexact line searches and it is examined by using different non-linear test functions with various dimensions.