New modification of the Hestenes-Stiefel with strong Wolfe line search

2021 ◽  
Author(s):  
Nur Athira Japri ◽  
Srimazzura Basri ◽  
Mustafa Mamat
Keyword(s):  
Line Search ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search

Two-Parameter Conjugate Gradient Projection Method and its Application

2014 ◽  
Vol 989-994 ◽  
pp. 1802-1805
Author(s):  
Hong Fang Cui
Keyword(s):  
Conjugate Gradient Method ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Linear Constraints ◽  
Convergence Criteria ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Two Parameter

On the basis of the conjugate gradient method CD, the artile builds a new two-parameter P-NCD projected conjugate gradient method, the article gives two-parameter P-NCD Conjugate Gradient Method drop projection and on the strong Wolfe line search in the principles of the convergence criteria, the new algorithm is applied to estimate the equation with linear constraints in the model instantiated test ,the results shows good results.

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 modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems

2017 ◽  
Vol 7 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Pro Kaelo ◽  
Sindhu Narayanan ◽  
M.V. Thuto
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid method.

Global convergence of a modified Fletcher–Reeves conjugate gradient method with Wolfe line search

2019 ◽  
Vol 13 (04) ◽  
pp. 2050081
Author(s):  
Badreddine Sellami ◽  
Mohamed Chiheb Eddine Sellami
Keyword(s):  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradients ◽  
Gradient Algorithm ◽  
Conjugacy Condition ◽  
Sufficient Descent Condition ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search

In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. we propose a modified Fletcher–Reeves (abbreviated FR) [Function minimization by conjugate gradients, Comput. J. 7 (1964) 149–154] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter [Formula: see text] is proposed. The parameter [Formula: see text] is computed by means of the conjugacy condition, thus an algorithm which is a positive multiplicative modification of the Hestenes and Stiefel (abbreviated HS) [Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sec. B 48 (1952) 409–436] algorithm is obtained, which produces a descent search direction at every iteration that the line search satisfies the Wolfe conditions. Under appropriate conditions, we show that the modified FR method with the strong Wolfe line search is globally convergent of uniformly convex functions. We also present extensive preliminary numerical experiments to show the efficiency of the proposed method.

A new hybrid conjugate gradient method of unconstrained optimization methods

2021 ◽  
pp. 2250070
Author(s):  
Chenna Nasreddine ◽  
Sellami Badreddine ◽  
Belloufi Mohammed
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Convex Combination ◽  
Optimization Methods ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

In this paper, we present a new hybrid method to solve a nonlinear unconstrained optimization problem by using conjugate gradient, which is a convex combination of Liu–Storey (LS) conjugate gradient method and Hager–Zhang (HZ) conjugate gradient method. This method possesses the sufficient descent property with Strong Wolfe line search and the global convergence with the strong Wolfe line search. In the end of this paper, we illustrate our method by giving some numerical examples.

scholarly journals A globally convergent hybrid conjugate gradient method with strong Wolfe conditions for unconstrained optimization

2019 ◽  
Vol 14 (1) ◽  
pp. 1-9
Author(s):  
P. Kaelo ◽  
P. Mtagulwa ◽  
M. V. Thuto
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Gradient Methods ◽  
Convergence Properties ◽  
Good Convergence ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Hybrid Conjugate Gradient Method

Abstract In this paper, we develop a new hybrid conjugate gradient method that inherits the features of the Liu and Storey (LS), Hestenes and Stiefel (HS), Dai and Yuan (DY) and Conjugate Descent (CD) conjugate gradient methods. The new method generates a descent direction independently of any line search and possesses good convergence properties under the strong Wolfe line search conditions. Numerical results show that the proposed method is robust and efficient.

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