scholarly journals A Spline Smoothing Newton Method for Semi-Infinite Minimax Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Li Dong ◽  
Bo Yu ◽  
Yu Xiao
Keyword(s):  
Newton Method ◽  
Large Scale ◽  
Minimax Problems ◽  
Smoothing Newton Method ◽  
Spline Smoothing ◽  
Smoothing Technique ◽  
Active Set ◽  
Discretization Methods ◽  
Numerical Tests ◽  
Infinite Programming

Based on discretization methods for solving semi-infinite programming problems, this paper presents a spline smoothing Newton method for semi-infinite minimax problems. The spline smoothing technique uses a smooth cubic spline instead of max function and only few components in the max function are computed; that is, it introduces an active set technique, so it is more efficient for solving large-scale minimax problems arising from the discretization of semi-infinite minimax problems. Numerical tests show that the new method is very efficient.

scholarly journals A Spline Smoothing Newton Method for L∞ Distance Regression with Bound Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Li Dong ◽  
Bo Yu
Keyword(s):  
Newton Method ◽  
Natural Generalization ◽  
Cubic Spline ◽  
Measured Data ◽  
Smoothing Newton Method ◽  
Spline Smoothing ◽  
Bound Constraints ◽  
Active Set ◽  
Aggregate Function ◽  
Orthogonal Distance Regression

Orthogonal distance regression is arguably the most common criterion for fitting a model to data with errors in the observations. It is not appropriate to force the distances to be orthogonal, when angular information is available about the measured data points. We consider here a natural generalization of a particular formulation of that problem which involves the replacement of l2 norm by l∞ norm. This criterion may be a more appropriate one in the context of accept/reject decisions for manufacture parts. For l∞ distance regression with bound constraints, we give a smoothing Newton method which uses cubic spline and aggregate function, to smooth max function. The main spline smoothing technique uses a smooth cubic spline instead of max function and only few components in the max function are computed; hence it acts also as an active set technique, so it is more efficient for the problem with large amounts of measured data. Numerical tests in comparison to some other methods show that the new method is very efficient.

A Smoothing Newton Method for Semi-Infinite Programming

2004 ◽  
Vol 30 (2-3) ◽  
pp. 169-194 ◽  
Author(s):  
Dong-Hui Li ◽  
Liqun Qi ◽  
Judy Tam ◽  
Soon-Yi Wu
Keyword(s):  
Newton Method ◽  
Smoothing Newton Method ◽  
Infinite Programming

scholarly journals A Generalized Inexact Newton Method for Inverse Eigenvalue Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weiping Shen
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Eigenvalue Problems ◽  
Generalized Newton Method ◽  
Inexact Newton Method ◽  
Numerical Tests ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue ◽  
Generalized Newton ◽  
Special Case

We propose a generalized inexact Newton method for solving the inverse eigenvalue problems, which includes the generalized Newton method as a special case. Under the nonsingularity assumption of the Jacobian matrices at the solutionc*, a convergence analysis covering both the distinct and multiple eigenvalue cases is provided and the quadratic convergence property is proved. Moreover, numerical tests are given in the last section and comparisons with the generalized Newton method are made.

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