scholarly journals A Modified Scaled Spectral-Conjugate Gradient-Based Algorithm for Solving Monotone Operator Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Auwal Bala Abubakar ◽  
Kanikar Muangchoo ◽  
Abdulkarim Hassan Ibrahim ◽  
Sunday Emmanuel Fadugba ◽  
Kazeem Olalekan Aremu ◽  
...  
Keyword(s):  
Global Convergence ◽  
Monotone Operator ◽  
Conjugate Gradient ◽  
Test Problems ◽  
Operator Equations ◽  
Numerical Examples ◽  
Monotonicity Assumption ◽  
Gradient Based ◽  
Spectral Conjugate Gradient ◽  
Search Directions

This paper proposes a modified scaled spectral-conjugate-based algorithm for finding solutions to monotone operator equations. The algorithm is a modification of the work of Li and Zheng in the sense that the uniformly monotone assumption on the operator is relaxed to just monotone. Furthermore, unlike the work of Li and Zheng, the search directions of the proposed algorithm are shown to be descent and bounded independent of the monotonicity assumption. Moreover, the global convergence is established under some appropriate assumptions. Finally, numerical examples on some test problems are provided to show the efficiency of the proposed algorithm compared to that of Li and Zheng.

Global convergence of a new spectral conjugate gradient by using Strong Wolfe line search

2015 ◽  
Vol 9 ◽  
pp. 3105-3117 ◽  
Author(s):  
Norhaslinda Zull ◽  
Mohd Rivaie ◽  
Mustafa Mamat ◽  
Zabidin Salleh ◽  
Zahrahtul Amani
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Line Search ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Spectral Conjugate Gradient

scholarly journals Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jinkui Liu ◽  
Youyi Jiang
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
New Method ◽  
Test Problems ◽  
Sufficient Descent Condition ◽  
Spectral Conjugate Gradient

A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent conditiongkTdk<−∥gk∥2. Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995) in contrast to the famous CD method, FR method, and PRP method.

scholarly journals A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohammed Yusuf Waziri ◽  
Jamilu Sabi’u
Keyword(s):  
Global Convergence ◽  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Systems Of Nonlinear Equations ◽  
Test Problems ◽  
Storage Requirement ◽  
Large Scale Problems ◽  
Derivative Free ◽  
Symmetric Systems

We suggest a conjugate gradient (CG) method for solving symmetric systems of nonlinear equations without computing Jacobian and gradient via the special structure of the underlying function. This derivative-free feature of the proposed method gives it advantage to solve relatively large-scale problems (500,000 variables) with lower storage requirement compared to some existing methods. Under appropriate conditions, the global convergence of our method is reported. Numerical results on some benchmark test problems show that the proposed method is practically effective.

scholarly journals A Modified Bat Algorithm with Conjugate Gradient Method for Global Optimization

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Huda I. Ahmed ◽  
Eman T. Hamed ◽  
Hamsa Th. Saeed Chilmeran
Keyword(s):  
Conjugate Gradient ◽  
Optimization Problems ◽  
Statistical Tests ◽  
Optimal Solution ◽  
Bat Algorithm ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Test Problems ◽  
Spectral Conjugate Gradient ◽  
Modified Bat Algorithm

Metaheuristic algorithms are used to solve many optimization problems. Firefly algorithm, particle swarm improvement, harmonic search, and bat algorithm are used as search algorithms to find the optimal solution to the problem field. In this paper, we have investigated and analyzed a new scaled conjugate gradient algorithm and its implementation, based on the exact Wolfe line search conditions and the restart Powell criterion. The new spectral conjugate gradient algorithm is a modification of the Birgin and Martínez method, a manner to overcome the lack of positive definiteness of the matrix defining the search direction. The preliminary computational results for a set of 30 unconstrained optimization test problems show that this new spectral conjugate gradient outperforms a standard conjugate gradient in this field and we have applied the newly proposed spectral conjugate gradient algorithm in bat algorithm to reach the lowest possible goal of bat algorithm. The newly proposed approach, namely, the directional bat algorithm (CG-BAT), has been then tested using several standard and nonstandard benchmarks from the CEC’2005 benchmark suite with five other algorithms and has been then tested using nonparametric statistical tests and the statistical test results show the superiority of the directional bat algorithm, and also we have adopted the performance profiles given by Dolan and More which show the superiority of the new algorithm (CG-BAT).

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