scholarly journals Preconditioning on subspace quasi-Newton method for large scale unconstrained optimization

2014 ◽  
Author(s):  
Hong Seng Sim ◽  
Wah June Leong ◽  
Fudziah Ismail
Keyword(s):  
Unconstrained Optimization ◽  
Newton Method ◽  
Large Scale ◽  
Large Scale Unconstrained Optimization ◽  
Quasi Newton

scholarly journals The Hybrid BFGS-CG Method in Solving Unconstrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Mohd Asrul Hery Ibrahim ◽  
Mustafa Mamat ◽  
Wah June Leong
Keyword(s):  
Unconstrained Optimization ◽  
Hybrid Method ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization ◽  
Quasi Newton

In solving large scale problems, the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Hence, a new hybrid method, known as the BFGS-CG method, has been created based on these properties, combining the search direction between conjugate gradient methods and quasi-Newton methods. In comparison to standard BFGS methods and conjugate gradient methods, the BFGS-CG method shows significant improvement in the total number of iterations and CPU time required to solve large scale unconstrained optimization problems. We also prove that the hybrid method is globally convergent.

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