View source for Models (Constrained) Nonlinear Least Squares Problems: cls prob, mgh prob and ls prob

{{Part Of Manual|title=TOMLAB Models|link=[[Models|TOMLAB Models]]}}
The TOMLAB bundle testprob provides three  sets  of test problems  for (constrained)  nonlinear least squares: <tt>cls_prob</tt>, <tt>mg_prob</tt> and <tt>ls_prob</tt>.

==An example of a (constrained) nonlinear least squares)==

The basic structure of a (constrained) nonlinear least squares problem is the following


<math>
\begin{array}{ll}\min\limits_{x} & f(x) = \frac{1}{2} r(x)^T r(x) \\&  \\s/t & \begin{array}{lcccl}x_{L} & \leq  & x   & \leq & x_{U}, \\b_{L} & \leq  & A x  & \leq & b_{U} \\c_{L} & \leq  & c(x) & \leq & c_{U} \\\end{array}\end{array}
</math>

where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>r(x) \in \mathbb{R}^M</math>,
<math>A \in \mathbb{R}^{m_1 \times n}</math>, <math>b_L,b_U \in
\mathbb{R}^{m_1}</math> and <math>c_L,c(x),c_U \in \mathbb{R}^{m_2}</math>. 

The following files are required to define a problem of this category in TOMLAB.

'''File: '''tomlab/quickguide/nllsQG r.m, nllsQG J.m

<pre>
r:	Residual  vector
J:	Jacobian  matrix
</pre>

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:

<source lang="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);
</source>

==cls_prob==

<tt>cls_prob</tt> 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:

<pre>
Prob	= probInit('cls_prob',1); 
Result  = tomRun('',Prob);
</pre>

==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:

<pre>
Prob	= probInit('mgh_prob',1); 
Result  = tomRun('',Prob);
</pre>

==ls_prob==

In <tt>ls_prob</tt> 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:

<pre>
Prob	= probInit('ls_prob',1); 
Result  = tomRun('',Prob);
</pre>