Inexact proximal memoryless quasi-Newton methods based on the Broyden family for minimizing composite functions

2021 ◽  
Vol 79 (1) ◽  
pp. 127-154
Author(s):  
Shummin Nakayama ◽  
Yasushi Narushima ◽  
Hiroshi Yabe
Keyword(s):  
Newton Methods ◽  
Composite Functions ◽  
Inexact Proximal ◽  
Quasi Newton ◽  
Broyden Family

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 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

scholarly journals A Broyden Class of Quasi-Newton Methods for Riemannian Optimization

2015 ◽  
Vol 25 (3) ◽  
pp. 1660-1685 ◽  
Author(s):  
Wen Huang ◽  
K. A. Gallivan ◽  
P.-A. Absil
Keyword(s):  
Newton Methods ◽  
Riemannian Optimization ◽  
Broyden Class ◽  
Quasi Newton

Quasi-Newton methods for saddlepoints

1985 ◽  
Vol 47 (4) ◽  
pp. 393-399 ◽  
Author(s):  
F. Biegler-König
Keyword(s):  
Newton Methods ◽  
Quasi Newton

Inexact Newton and quasi-Newton methods for the output feedback pole assignment problem

2013 ◽  
Vol 33 (3) ◽  
pp. 517-542 ◽  
Author(s):  
El-Sayed M. E. Mostafa ◽  
Mohamed A. Tawhid ◽  
Eman R. Elwan
Keyword(s):  
Output Feedback ◽  
Assignment Problem ◽  
Pole Assignment ◽  
Newton Methods ◽  
Quasi Newton

scholarly journals Multi-step quasi-Newton methods for optimization

1994 ◽  
Vol 50 (1-3) ◽  
pp. 305-323 ◽  
Author(s):  
J.A. Ford ◽  
I.A. Moghrabi
Keyword(s):  
Newton Methods ◽  
Quasi Newton

Phase equilibrium calculations with quasi-Newton methods

2015 ◽  
Vol 406 ◽  
pp. 194-208 ◽  
Author(s):  
Dan Vladimir Nichita ◽  
Martin Petitfrere
Keyword(s):  
Phase Equilibrium ◽  
Newton Methods ◽  
Quasi Newton ◽  
Equilibrium Calculations
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