A Modified Hestenes-Stiefel Conjugate Gradient Algorithm for Large-Scale Optimization

2013 ◽  
Vol 34 (8) ◽  
pp. 914-937 ◽  
Author(s):  
Gonglin Yuan ◽  
Maojun Zhang
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Large Scale Optimization ◽  
Scale Optimization

A new three-term spectral conjugate gradient algorithm with higher numerical performance for solving large scale optimization problems based on Quasi-Newton equation

2021 ◽  
pp. 2150053
Author(s):  
Jie Guo ◽  
Zhong Wan
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Large Scale Optimization ◽  
Newton Equation ◽  
Numerical Performance ◽  
Scale Optimization ◽  
Quasi Newton

A new spectral three-term conjugate gradient algorithm in virtue of the Quasi-Newton equation is developed for solving large-scale unconstrained optimization problems. It is proved that the search directions in this algorithm always satisfy a sufficiently descent condition independent of any line search. Global convergence is established for general objective functions if the strong Wolfe line search is used. Numerical experiments are employed to show its high numerical performance in solving large-scale optimization problems. Particularly, the developed algorithm is implemented to solve the 100 benchmark test problems from CUTE with different sizes from 1000 to 10,000, in comparison with some similar ones in the literature. The numerical results demonstrate that our algorithm outperforms the state-of-the-art ones in terms of less CPU time, less number of iteration or less number of function evaluation.

scholarly journals A conjugate gradient algorithm and its application in large-scale optimization problems and image restoration

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Gonglin Yuan ◽  
Tingting Li ◽  
Wujie Hu
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Trust Region ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Smooth Functions ◽  
Nonsmooth Functions ◽  
Large Scale Unconstrained Optimization

Abstract To solve large-scale unconstrained optimization problems, a modified PRP conjugate gradient algorithm is proposed and is found to be interesting because it combines the steepest descent algorithm with the conjugate gradient method and successfully fully utilizes their excellent properties. For smooth functions, the objective algorithm sufficiently utilizes information about the gradient function and the previous direction to determine the next search direction. For nonsmooth functions, a Moreau–Yosida regularization is introduced into the proposed algorithm, which simplifies the process in addressing complex problems. The proposed algorithm has the following characteristics: (i) a sufficient descent feature as well as a trust region trait; (ii) the ability to achieve global convergence; (iii) numerical results for large-scale smooth/nonsmooth functions prove that the proposed algorithm is outstanding compared to other similar optimization methods; (iv) image restoration problems are done to turn out that the given algorithm is successful.

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