A Second Derivative SQP Method: Local Convergence and Practical Issues

2010 ◽  
Vol 20 (4) ◽  
pp. 2049-2079 ◽  
Author(s):  
Nicholas I. M. Gould ◽  
Daniel P. Robinson
Keyword(s):  
Local Convergence ◽  
Second Derivative ◽  
Sqp Method

scholarly journals Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yonghui Ling ◽  
Xiubin Xu ◽  
Shaohua Yu
Keyword(s):  
Banach Spaces ◽  
Local Convergence ◽  
Nonlinear Operator ◽  
Convergence Criterion ◽  
Second Derivative ◽  
Operator Equations ◽  
Convergence Ball ◽  
Nonlinear Operator Equations ◽  
Steffensen’S Method ◽  
Convergence Problems

The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.

A second-derivative SQP method with a 'trust-region-free' predictor step

2011 ◽  
Vol 32 (2) ◽  
pp. 580-601 ◽  
Author(s):  
N. I. M. Gould ◽  
D. P. Robinson
Keyword(s):  
Trust Region ◽  
Second Derivative ◽  
Sqp Method ◽  
Predictor Step

scholarly journals Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains

2019 ◽  
Vol 33 (1) ◽  
pp. 21-40
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Local Convergence ◽  
Uniqueness Result ◽  
Second Derivative ◽  
Numerical Examples ◽  
The Third ◽  
Lipschitz Constants ◽  
Local Convergence Analysis ◽  
Third Derivative

AbstractWe present a local convergence analysis of the super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier studies was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the super-Halley-like method by using hypotheses up to the second derivative. We also provide: a computable error on the distances involved and a uniqueness result based on Lipschitz constants. Numerical examples are also presented in this study.

scholarly journals A Second Derivative SQP Method: Global Convergence

2010 ◽  
Vol 20 (4) ◽  
pp. 2023-2048 ◽  
Author(s):  
Nicholas I. M. Gould ◽  
Daniel P. Robinson
Keyword(s):  
Global Convergence ◽  
Second Derivative ◽  
Sqp Method

A Nonmonotone Filter SQP Method: Local Convergence and Numerical Results

2015 ◽  
Vol 25 (3) ◽  
pp. 1885-1911 ◽  
Author(s):  
Nicholas I. M. Gould ◽  
Yueling Loh ◽  
Daniel P. Robinson
Keyword(s):  
Local Convergence ◽  
Numerical Results ◽  
Sqp Method

On the Local Convergence of a Penalty-Function-Free SQP Method

2014 ◽  
Vol 35 (5) ◽  
pp. 623-647 ◽  
Author(s):  
Chungen Shen ◽  
Wenqiong Shao ◽  
Wenjuan Xue
Keyword(s):  
Penalty Function ◽  
Local Convergence ◽  
Sqp Method
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