A Hybrid of Quasi-Newton Method with CG Method for Unconstrained Optimization

Conjugate gradient (CG) method is one of iterative techniques prominently used in solving unconstrained optimization problems due to its simplicity, low memory storage, and good convergence analysis This paper presents a new hybrid conjugate gradient method, named NRM1 method The method is analyzed under the exact and inexact line searches in given conditions Theoretically, proofs show that the NRM1 method satisfies the sufficient descent condition with both line searches The computational result indicates that NRM1 method is capable in solving the standard unconstrained optimization problems used On the other hand, the NRM1 method performs better under inexact line search compared with exact line search

https://iopscience.iop.org/article/10.1088/1742-6596/890/1/012106/pdf

Performance comparison of a new hybrid conjugate gradient method under exact and inexact line searches

One of the popular approaches in modifying the Conjugate Gradient (CG) Method is hybridization. In this paper, a new hybrid CG is introduced and its performance is compared to the classical CG method which are Rivaie-Mustafa-Ismail-Leong (RMIL) and Syarafina-Mustafa-Rivaie (SMR) methods. The proposed hybrid CG is evaluated as a convex combination of RMIL and SMR method. Their performance are analyzed under the exact line search. The comparison performance showed that the hybrid CG is promising and has outperformed the classical CG of RMIL and SMR in terms of the number of iterations and central processing unit per time.

http://ijain.org/index.php/IJAIN/article/download/356/ijain_v5i2_p150-159

A comparison on classical-hybrid conjugate gradient method under exact line search

The conjugate gradient (CG) method is one of the optimization methods that are often used in practical applications. The continuous and numerous studies conducted on the CG method have led to vast improvements in its convergence properties and efficiency. In this paper, a new CG method possessing the sufficient descent and global convergence properties is proposed. The efficiency of the new CG algorithm relative to the existing CG methods is evaluated by testing them all on a set of test functions using MATLAB. The tests are measured in terms of iteration numbers and CPU time under strong Wolfe line search. Overall, this new method performs efficiently and comparable to the other famous methods.

https://iopscience.iop.org/article/10.1088/1742-6596/890/1/012105/pdf

A conjugate gradient method with descent properties under strong Wolfe line search

Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations

https://iopscience.iop.org/article/10.1088/1742-6596/890/1/012108/pdf

A new modified conjugate gradient coefficient for solving system of linear equations

Conjugate gradient (CG) method is a line search algorithm mostly known for its wide application in solving unconstrained optimization problems. Its low memory requirements and global convergence properties makes it one of the most preferred method in real life application such as in engineering and business. In this paper, we present a new CG method based on AMR* and CD method for solving unconstrained optimization functions. The resulting algorithm is proven to have both the sufficient descent and global convergence properties under inexact line search. Numerical tests are conducted to assess the effectiveness of the new method in comparison to some previous CG methods. The results obtained indicate that our method is indeed superior.

A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

The conjugate gradient (CG) method is a well-known solver for large-scale unconstrained optimization problems. In this paper, a modified CG method based on AMR* and CD method is presented. The resulting algorithm for the new CG method is proved to be globally convergent under exact line search both under some mild conditions. Comparisons of numerical performance are made involving the new method and four other CG methods. The results show that the proposed method is more efficient.

A modified conjugate gradient coefficient under exact line search for unconstrained optimization

The conjugate gradient (CG) method is one of the most prominent methods for solving linear and nonlinear problems in optimization. In this paper, we propose a CG method with sufficient descent property under strong Wolfe line search. The proposed CG method is then applied to solve systems of linear equations. The numerical results obtained from the tests are evaluated based on number iteration and CPU time and then analyzed through performance profile. In order to examine its efficiency, the performance of our CG formula is compared to that of other CG methods. The results show that the proposed CG formula has better performance than the other tested CG methods.  

/pdf/an-application-of-conjugate-gradient-method-under-strong-227whznrhi.pdf

An application of conjugate gradient method under strong Wolfe line search for solving unconstrained optimization

In this paper, we focus on the steepest descent and quasi-Newton method in solving unconstrained optimization problem. Therefore, we develop a new search direction for hybrid BFGS-ZMRI method with global convergence properties. Based on the numerical result, our method shows significant improvement in the number of iteration and CPU time.In this paper, we focus on the steepest descent and quasi-Newton method in solving unconstrained optimization problem. Therefore, we develop a new search direction for hybrid BFGS-ZMRI method with global convergence properties. Based on the numerical result, our method shows significant improvement in the number of iteration and CPU time.

Hybrid BFGS-ZMRI methods with global convergence properties

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Papers

A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

A modified conjugate gradient coefficient under exact line search for unconstrained optimization

An application of conjugate gradient method under strong Wolfe line search for solving unconstrained optimization

Hybrid BFGS-ZMRI methods with global convergence properties