A Parallel Block Scaled Gradient Method With Decentralized Step-Size For Block Additive Unconstrained Optimization Problems Of Large Distributed Systems

2008 ◽  
Vol 5 (1) ◽  
pp. 104-115 ◽  
Author(s):  
Shin-Yeu Lin ◽  
Shieh-Shing Lin
Keyword(s):  
Distributed Systems ◽  
Unconstrained Optimization ◽  
Gradient Method ◽  
Optimization Problems ◽  
Step Size ◽  
Unconstrained Optimization Problems

A Simulated Annealing-Based Barzilai–Borwein Gradient Method for Unconstrained Optimization Problems

2019 ◽  
Vol 36 (04) ◽  
pp. 1950017 ◽  
Author(s):  
Wen-Li Dong ◽  
Xing Li ◽  
Zheng Peng
Keyword(s):  
Simulated Annealing ◽  
Unconstrained Optimization ◽  
Gradient Method ◽  
Line Search ◽  
High Efficiency ◽  
Optimization Problems ◽  
Search Technique ◽  
Unconstrained Optimization Problems ◽  
Armijo Line Search ◽  
Line Search Technique

In this paper, we propose a simulated annealing-based Barzilai–Borwein (SABB) gradient method for unconstrained optimization problems. The SABB method accepts the Barzilai–Borwein (BB) step by a simulated annealing rule. If the BB step cannot be accepted, the Armijo line search is used. The global convergence of the SABB method is established under some mild conditions. Numerical experiments indicate that, compared to some existing BB methods using nonmonotone line search technique, the SABB method performs well with high efficiency.

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.

scholarly journals A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 227
Author(s):  
Zabidin Salleh ◽  
Ghaliah Alhamzi ◽  
Ibitsam Masmali ◽  
Ahmad Alhawarat
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Numerical Results ◽  
New Method ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural networks, image restoration, etc. Many complicated methods are proposed to solve these optimization functions in two or three terms. In this paper, we propose a simple, easy, efficient, and robust conjugate gradient method. The new method is constructed based on the Liu and Storey method to overcome the convergence problem and descent property. The new modified method satisfies the convergence properties and the sufficient descent condition under some assumptions. The numerical results show that the new method outperforms famous CG methods such as CG-Descent5.3, Liu and Storey, and Dai and Liao. The numerical results include the number of iterations and CPU time.

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