scholarly journals Application of spectral conjugate gradient methods for solving unconstrained optimization problems

2020 ◽  
Vol 10 (2) ◽  
pp. 198-205
Author(s):  
Sulaiman Mohammed Ibrahim ◽  
Usman Abbas Yakubu ◽  
Mustafa Mamat
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Computational Cost ◽  
Real Life ◽  
Gradient Methods ◽  
Nonlinear Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems

Conjugate gradient (CG) methods are among the most efficient numerical methods for solving unconstrained optimization problems. This is due to their simplicty and  less computational cost in solving large-scale nonlinear problems. In this paper, we proposed some spectral CG methods using the classical CG search direction. The proposed methods are applied to real-life problems in regression analysis. Their convergence proof was establised under exact line search. Numerical results has shown that the proposed methods are efficient and promising.

A NEW COEFFICIENT OF CONJUGATE GRADIENT METHODS FOR NONLINEAR UNCONSTRAINED OPTIMIZATION

2016 ◽  
Vol 78 (6-4) ◽  
Author(s):  
Nur Syarafina Mohamed ◽  
Mustafa Mamat ◽  
Fatma Susilawati Mohamad ◽  
Mohd Rivaie
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Standard Test ◽  
Processing Unit ◽  
Central Processing ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Nonlinear Unconstrained Optimization

Conjugate gradient (CG) methods are widely used in solving nonlinear unconstrained optimization problems such as designs, economics, physics and engineering due to its low computational memory requirement. In this paper, a new modifications of CG coefficient ( ) which possessed global convergence properties is proposed by using exact line search. Based on the number of iterations and central processing unit (CPU) time, the numerical results show that the new  performs better than some other well known CG methods under some standard test functions.

scholarly journals Solving a large scale nonlinear unconstrained optimization problems by using new coefficient of conjugate gradient method with exact line search direction

2018 ◽  
Vol 7 (3.28) ◽  
pp. 92
Author(s):  
Talat Alkouli ◽  
Mustafa Mamat ◽  
Mohd Rivaie ◽  
Puspa Liza Ghazali
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

In this paper, an efficient modification of nonlinear conjugate gradient method and an associated implementation, based on an exact line search, are proposed and analyzed to solve large-scale unconstrained optimization problems. The method satisfies the sufficient descent property. Furthermore, global convergence result is proved. Computational results for a set of unconstrained optimization test problems, some of them from CUTE library, showed that this new conjugate gradient algorithm seems to converge more stable and outperforms the other similar methods in many situations.   

scholarly journals Penalty Algorithm Based on Three-Term Conjugate Gradient Method for Unconstrained Optimization Portfolio Management Problems

2019 ◽  
pp. 1-13
Author(s):  
Samson Akinwale ◽  
O. O. Okundalaye
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Portfolio Management ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Computational Cost ◽  
Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Management Problems

In a class of solving unconstrained optimization problems, the conjugate gradient method has been proved to be efficient by researchers' due to it's smaller storage requirements and computational cost. Then, a class of penalty algorithms based on three-term conjugate gradient methods was developed and extend to and solution of an unconstrained minimization portfolio management problems, where the objective function is a piecewise quadratic polynomial. By implementing the proposed algorithm to solve some selected unconstrained optimization problems, resulted in improvement in the total number of iterations and CPU time. It was shown that this algorithm is promising.

scholarly journals The Hybrid BFGS-CG Method in Solving Unconstrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mohd Asrul Hery Ibrahim ◽  
Mustafa Mamat ◽  
Wah June Leong
Keyword(s):  
Unconstrained Optimization ◽  
Hybrid Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization ◽  
Quasi Newton

In solving large scale problems, the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Hence, a new hybrid method, known as the BFGS-CG method, has been created based on these properties, combining the search direction between conjugate gradient methods and quasi-Newton methods. In comparison to standard BFGS methods and conjugate gradient methods, the BFGS-CG method shows significant improvement in the total number of iterations and CPU time required to solve large scale unconstrained optimization problems. We also prove that the hybrid method is globally convergent.

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

2018 ◽  
Vol 7 (3.28) ◽  
pp. 84 ◽  
Author(s):  
Nurul Aini ◽  
Nurul Hajar ◽  
Mohd Rivaie ◽  
Mustafa Mamat
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Mild Conditions ◽  
Exact Line Search ◽  
Unconstrained Optimization Problems ◽  
Numerical Performance ◽  
Large Scale 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.  

scholarly journals Two-versions of descent conjugate gradient methods for large-scale unconstrained optimization

2021 ◽  
Vol 22 (3) ◽  
pp. 1643
Author(s):  
Hawraz N. Jabbar ◽  
Basim A. Hassan
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Taylor Series Expansion ◽  
Conjugate Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Gradient Type ◽  
Large Scale Unconstrained Optimization

<p>The conjugate gradient methods are noted to be exceedingly valuable for solving large-scale unconstrained optimization problems since it needn't the storage of matrices. Mostly the parameter conjugate is the focus for conjugate gradient methods. The current paper proposes new methods of parameter of conjugate gradient type to solve problems of large-scale unconstrained optimization. A Hessian approximation in a diagonal matrix form on the basis of second and third-order Taylor series expansion was employed in this study. The sufficient descent property for the proposed algorithm are proved. The new method was converged globally. This new algorithm is found to be competitive to the algorithm of fletcher-reeves (FR) in a number of numerical experiments.</p>

scholarly journals A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Can Li
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Type Method ◽  
Unconstrained Optimization Problems ◽  
Feasible Direction Method ◽  
Gradient Type ◽  
Large Scale Unconstrained Optimization ◽  
Nonnegative Constraints

We are concerned with the nonnegative constraints optimization problems. It is well known that the conjugate gradient methods are efficient methods for solving large-scale unconstrained optimization problems due to their simplicity and low storage. Combining the modified Polak-Ribière-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems. If the current iteration is a feasible point, the direction generated by the proposed method is always a feasible descent direction at the current iteration. Under appropriate conditions, we show that the proposed method is globally convergent. We also present some numerical results to show the efficiency of the proposed method.

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