Keywords : inexact line search


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.
 

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 .
 

New Variable Metric Algorithm by The Mean of 2nd Order Quasi-Newton Condition

Abbas Y. Al-Bayati; Runak M. Abdullah

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 2, Pages 35-41
DOI: 10.33899/csmj.2011.163639

In this paper a new class of Quasi-Newton update for solving unconstrained nonlinear optimization problem is proposed. In this work we suggested a new formula for the variable metric update with  a new quasi-Newton condition used for the symmetric rank two formula.
Finally, a numerical study is reported in which the performance of this new algorithm is compared to that of various members of the unmodified family. Numerical experiments indicate that this new algorithm is effective and superior to the standard BFGS and DFP algorithms, with respect to the number of functions evaluations (NOF) and number of iterations (NOI).
 

A New hybrid generalized CG- method for non-linear functions

Abbas Y. Al-Bayati; Hamsa Th. Chilmerane

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 1, Pages 13-24
DOI: 10.33899/csmj.2010.163843

In this paper a new extended generalized conjugate gradient algorithm is proposed for unconstrained optimization, which is considered as anew inverse hyperbolic model .In order to improve the rate of convergence of the new technique, a new hybrid technique between the standard F/R CG-method and Sloboda CG-method using quadratic and non-quadratic models is proposed by using exact and inexact line searches. This method is more efficient and robust when applied on number of well-known nonlinear test function.
 

A New Family of Spectral CG-Algorithm

Abbas Y. Al-Bayati; Runak M. Abdullah

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 1, Pages 69-80
DOI: 10.33899/csmj.2008.163950

A new family of  CG –algorithms for large-scale unconstrained optimization is introduced in this paper using the spectral scaling for the search directions, which is a generalization of the spectral gradient method proposed by Raydan [14].
Two modifications of the method are presented, one using Barzilai line search, and the others  take  at each iteration (where  is step- size). In both cases tested for the  Wolfe conditions, eleven test problems with different dimensions are used to compare these algorithms against the  well-known Fletcher –Revees CG-method, with obtaining a robust numerical results.