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13 NLLS Problem
The
constrained nonlinear least squares (
cls) problem
is defined as
|
|
|
|
|
s/t |
xL |
≤ |
x |
≤ |
xU, |
bL |
≤ |
A x |
≤ |
bU |
cL |
≤ |
c(x) |
≤ |
cU |
|
|
(15) |
where
x,
xL,
xU Rn,
r(
x)
RM,
A Rm1 × n,
bL,
bU
Rm1 and
cL,
c(
x),
cU Rm2. The
following file defines and solves a problem in TOMLAB.
The following files define a problem in TOMLAB.
File: tomlab/quickguide/nllsQG_r.m, nllsQG_J.m
r: Residual vector
J: Jacobian matrix
The following file illustrates how to solve an NLLS problem in
TOMLAB. Also view the m-files specified above for more
information.
File: tomlab/quickguide/nllsQG.m
Open the file for viewing, and execute nllsQG in Matlab.
% nllsQG is a small example problem for defining and solving
% nonlinear least squares using the TOMLAB format.
Name='Gisela';
t = [0.25; 0.5; 0.75; 1; 1.5; 2; 3; 4; 6; 8; 12; 24; 32; 48; 54; 72; 80;...
96; 121; 144; 168; 192; 216; 246; 276; 324; 348; 386];
y = [30.5; 44; 43; 41.5; 38.6; 38.6; 39; 41; 37; 37; 24; 32; 29; 23; 21;...
19; 17; 14; 9.5; 8.5; 7; 6; 6; 4.5; 3.6; 3; 2.2; 1.6];
x_0 = [6.8729, 0.0108, 0.1248]';
% See help clsAssign for more information.
Prob = clsAssign('nllsQG_r', 'nllsQG_J', [], [], [], Name, x_0, ...
y, t);
% Parameter which is passed to r and J routines.
Prob.uP = 5;
Result = tomRun('clsSolve', Prob, 1);
%Result = tomRun('nlssol', Prob, 1);
% Any nonlinear solver can be used. TOMLAB automatically
% uses gateway routines for problem mapping.
%Result = tomRun('filterSQP', Prob, 1);
%Result = tomRun('knitro', Prob, 1);
%Result = tomRun('conopt', Prob, 1);
%Result = tomRun('snopt', Prob, 1);
%Result = tomRun('npsol', Prob, 1);
%Result = tomRun('minos', Prob, 1);
%Result = tomRun('oqnlp', Prob, 1);
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