scholarly journals Memoryless quasi-Newton methods based on spectral-scaling Broyden family for unconstrained optimization

2019 ◽  
Vol 15 (4) ◽  
pp. 1773-1793
Author(s):  
Shummin Nakayama ◽  
◽  
Yasushi Narushima ◽  
Hiroshi Yabe ◽  
◽  
...  
Keyword(s):  
Unconstrained Optimization ◽  
Newton Methods ◽  
Quasi Newton ◽  
Broyden Family

Parallel quasi-Newton methods for unconstrained optimization

1988 ◽  
Vol 42 (1-3) ◽  
pp. 273-306 ◽  
Author(s):  
Richard H. Byrd ◽  
Robert B. Schnabel ◽  
Gerald A. Shultz
Keyword(s):  
Unconstrained Optimization ◽  
Newton Methods ◽  
Quasi Newton

scholarly journals Numerical Experience with Damped Quasi-Newton Optimization Methods when the Objective Function is Quadratic

2012 ◽  
Vol 16 ◽  
pp. 1 ◽  
Author(s):  
Mehiddin Al-Baali ◽  
Anton Purnama
Keyword(s):  
Convergence Property ◽  
Quadratic Function ◽  
Optimization Methods ◽  
Newton Methods ◽  
Objective Functions ◽  
Numerical Experience ◽  
Damped Technique ◽  
Quasi Newton ◽  
Broyden Family

A class of damped quasi-Newton methods for nonlinear optimization has recently been proposed by extending the damped-technique of Powell for the BFGS method to the Broyden family of quasi-Newton methods. It has been shown that this damped class has the global and superlinear convergence property that a restricted class of 'undamped' methods has for convex objective functions in unconstrained optimization. To test this result, we applied several members of the Broyden family and their corresponding damped methods to a simple quadratic function and observed several useful features of the damped-technique. These observations and other numerical experiences are described in this paper. The important role of the damped-technique is shown not only for enforcing the above convergence property, but also for improving the performance of efficient, inefficient and divergent undamped methods substantially (significantly in the latter case). Thus, some appropriate ways for employing the damped-technique are suggested. 

scholarly journals A new variants of quasi-newton equation based on the quadratic function for unconstrained optimization

2020 ◽  
Vol 19 (2) ◽  
pp. 701
Author(s):  
Basim Abbas Hassan ◽  
Mohammed W. Taha
Keyword(s):  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Quadratic Function ◽  
New Method ◽  
Newton Methods ◽  
Newton Equation ◽  
Globally Convergent ◽  
Quasi Newton

<p>The focus for quasi-Newton methods is the quasi-Newton equation. A new quasi-Newton equation is derived for quadratic function. Then, based on this new quasi-Newton equation, a new quasi-Newton updating formulas are presented. Under appropriate conditions, it is shown that the proposed method is globally convergent. Finally, some numerical experiments are reported which verifies the effectiveness of the new method.</p>

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