scholarly journals Spectral Three-Term Constrained Conjugate Gradient Algorithm for Function Minimizations

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Huda I. Ahmed ◽  
Rana Z. Al-Kawaz ◽  
Abbas Y. Al-Bayati
Keyword(s):  
Global Convergence ◽  
Constrained Optimization ◽  
Conjugate Gradient ◽  
Line Search ◽  
Convergence Property ◽  
Optimization Methods ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Global Convergence Property ◽  
Wolfe Line Search

In this work, we tend to deal within the field of the constrained optimization methods of three-term Conjugate Gradient (CG) technique which is primarily based on Dai–Liao (DL) formula. The new proposed technique satisfies the conjugacy property and the descent conditions of Karush–Kuhn–Tucker (K.K.T.). Our planned constrained technique uses the robust Wolfe line search condition with some assumptions. We tend to prove the global convergence property of the new planned technique. Numeral comparisons for (30-thirty) constrained optimization issues make sure the effectiveness of the new planned formula.

New hyrid conjugate gradient method as a convex combination of HZ and CD methods

2021 ◽  
pp. 2150187
Author(s):  
Amira Hamdi ◽  
Badreddine Sellami ◽  
Mohammed Belloufi
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Convex Combination ◽  
Gradient Algorithm ◽  
Unconstrained Optimization Problems ◽  
Gradient Parameter ◽  
Sufficient Descent ◽  
Wolfe Line Search

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems, the conjugate gradient parameter [Formula: see text] is computed as a convex combination of [Formula: see text] and [Formula: see text]. Under the wolfe line search, we prove the sufficient descent and the global convergence. Numerical results are reported to show the effectiveness of our procedure.

scholarly journals A New Hybrid Algorithm for Convex Nonlinear Unconstrained Optimization

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Eman T. Hamed ◽  
Huda I. Ahmed ◽  
Abbas Y. Al-Bayati
Keyword(s):  
Hybrid Algorithm ◽  
Line Search ◽  
Convergence Property ◽  
High Scale ◽  
Descent Property ◽  
Global Convergence Property ◽  
Wolfe Line Search ◽  
Nonlinear Unconstrained Optimization ◽  
Quasi Newton ◽  
Algorithmic Rule

In this study, we tend to propose a replacement hybrid algorithmic rule which mixes the search directions like Steepest Descent (SD) and Quasi-Newton (QN). First, we tend to develop a replacement search direction for combined conjugate gradient (CG) and QN strategies. Second, we tend to depict a replacement positive CG methodology that possesses the adequate descent property with sturdy Wolfe line search. We tend to conjointly prove a replacement theorem to make sure global convergence property is underneath some given conditions. Our numerical results show that the new algorithmic rule is powerful as compared to different standard high scale CG strategies.

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 A Mixed Spectral CD-DY Conjugate Gradient Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Liu Jinkui ◽  
Du Xianglin ◽  
Wang Kairong
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Descent Method ◽  
Unconstrained Optimization Problems ◽  
Global Convergence Property ◽  
Wolfe Line Search ◽  
Spectral Conjugate Gradient

A mixed spectral CD-DY conjugate descent method for solving unconstrained optimization problems is proposed, which combines the advantages of the spectral conjugate gradient method, the CD method, and the DY method. Under the Wolfe line search, the proposed method can generate a descent direction in each iteration, and the global convergence property can be also guaranteed. Numerical results show that the new method is efficient and stationary compared to the CD (Fletcher 1987) method, the DY (Dai and Yuan 1999) method, and the SFR (Du and Chen 2008) method; so it can be widely used in scientific computation.

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