Newton-Raphson method with linear constraints
newtRaph.m
A Matlab implementation of the Newton-Raphson method with linear constraints
(c) Michael Mauersberger 2021 (v0.1), 2023 (v1.0, v1.1), LGPL License v2.1
Newton-Raphson method with constraints for finding function roots.
Damping coefficient helps to find a feasible solution.
Number of sweep points help to set a new initial searching point on the axis between the minimum and maximum of the domain.
Search ends if function tolerance or argument tolerance has been reached.
Linear constraints are applied in the form A*x <= b
via writing back the arguments to the constraint (done by means of QR decomposition and a pseudo-inverse).
References:
Wikipedia - "Newtonverfahren" (German), "Newton's method" (English)
Examples
Damping coefficient
[xVal,fVal,it,ex] = newtRaph(@(x)(x.^3-2*x+2),0,[],[],[],[],1e-10,1e-10,100,.0,'cent',1e-10,2)
xVal = 8.2740e-08
fVal = 2.0000
it = 100
ex = -2
[xVal,fVal,it,ex] = newtRaph(@(x)(x.^3-2*x+2),0,[],[],[],[],1e-10,1e-10,100,.2,'cent',1e-10,2)
xVal = -1.7693
fVal = 7.6439e-11
it = 24
ex = 0
Linear constraint
[xVal,fVal,it,ex] = newtRaph(@(x)(5*(x(1)+1)^2+x(2)^2-2*x(2)),[0 1],[],[],[],[],1e-10,1e-10,100,.2,'forw',1e-10,2)
xVal = [-0.5528 1.0000]
fVal = 8.3129e-11
it = 16
ex = 0
[xVal,fVal,it,ex] = newtRaph(@(x)(5*(x(1)+1)^2+x(2)^2-2*x(2)),[0 1],[],[],[-1 -1],[-.8],1e-8,1e-10,100,.2,'forw',1e-10,2)
xVal = [-0.5878 1.3878]
fVal = 8.1014e-09
it = 64
ex = 0
Number of sweep points
[xVal,fVal,it,ex] = newtRaph(@(x)((x.^2-3)*(x-1)-5*exp(-100*(x+.5)^2)),0,-1,0,[],[],1e-8,1e-10,100,.2,'cent',1e-10,2)
xVal = -2.6000
fVal = 4.0000
it = 3
ex = -2
[xVal,fVal,it,ex] = newtRaph(@(x)((x.^2-3)*(x-1)-5*exp(-100*(x+.5)^2)),0,-1,0,[],[],1e-8,1e-10,100,.2,'cent',1e-10,4)
xVal = -0.4544
fVal = 7.1891e-09
it = 20
ex = 0
Citar como
Michael Mauersberger (2024). Newton-Raphson method with linear constraints (https://github.com/m-mauersberger/NewtRaphConMatlab/releases/tag/v1.1), GitHub. Recuperado .
Compatibilidad con la versión de MATLAB
Compatibilidad con las plataformas
Windows macOS LinuxEtiquetas
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Descubra Live Editor
Cree scripts con código, salida y texto formateado en un documento ejecutable.
Versión | Publicado | Notas de la versión | |
---|---|---|---|
1.1 | See release notes for this release on GitHub: https://github.com/m-mauersberger/NewtRaphConMatlab/releases/tag/v1.1 |
||
1.0 | See release notes for this release on GitHub: https://github.com/m-mauersberger/NewtRaphConMatlab/releases/tag/v1.0 |
||
0.9 |