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10 Nonlinear Least Squares Problems
The TOMLAB bundle testprob provides three sets of test problems for
(constrained) nonlinear least squares:
cls_prob,
mgh_prob and
ls_prob.
10.1 An example of a (constrained) nonlinear least squares
The basic structure of a (constrained) nonlinear least squares problem is the following
|
|
|
|
| |
|
| s/t |
| xL |
≤ |
x |
≤ |
xU, |
| bL |
≤ |
A x |
≤ |
bU |
| cL |
≤ |
c(x) |
≤ |
cU |
|
|
(12) |
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 are required to define a problem of this category 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
An example of a problem of this class, (that is also found in the TOMLAB Quickguide) is nllsQG:
% 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);
10.2 cls_prob
cls_prob consists of 45 constrained nonlinear least squares test problems
with up to 14 variables and a mixture of linear and nonlinear constraints.
In order to define this problem and solve it execute the following in Matlab:
Prob = probInit('cls_prob',1);
Result = tomRun('',Prob);
10.3 mgh_prob
In
mgh_prob there are 35 nonlinear least squares (More, Garbow, Hillstrom) test problems
with up to 40 variables.
In order to define this problem and solve it execute the following in Matlab:
Prob = probInit('mgh_prob',1);
Result = tomRun('',Prob);
In
ls_prob there are 15 nonlinear least squares test problems
with up to 20 variables.
In order to define this problem and solve it execute the following in Matlab:
Prob = probInit('ls_prob',1);
Result = tomRun('',Prob);
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