Models Linear Least Squares Problems: lls prob: Difference between revisions
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where <math>x, x_L, x_U \in \ | where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>d \in \mathbb{R}^M</math>, <math>C \in | ||
\ | \mathbb{R}^{M \times n}</math>, <math>A \in \mathbb{R}^{m_1 \times n}</math> and | ||
<math>b_L,b_U \in \ | <math>b_L,b_U \in \mathbb{R}^{m_1}</math>. | ||
An example of a problem of this class, (that is also found in the TOMLAB quickguide) is llsQG: | An example of a problem of this class, (that is also found in the TOMLAB quickguide) is llsQG: |
Revision as of 13:57, 8 December 2011
This page is part of TOMLAB Models. See TOMLAB Models. |
In lls_prob there are two linear least squares test problems with about 10 variables and a few constraints. In order to define the first problem and solve it execute the following in Matlab:
Prob = probInit('lls_prob',1); Result = tomRun('',Prob);
The basic structure of a general linear least squares problem is:
where , , , and .
An example of a problem of this class, (that is also found in the TOMLAB quickguide) is llsQG:
File: tomlab/quickguide/llsQG.m
% llsQG is a small example problem for defining and solving
% linear least squares using the TOMLAB format.
Name='LSSOL test example'; % Problem name, not required.
n = 9;
x_L = [-2 -2 -inf, -2*ones(1,6)]'; % Lower bounds on x
x_U = 2*ones(9,1); % Upper bounds on x
% Matrix defining linear constraints
A = [ ones(1,8) 4; 1:4,-2,1 1 1 1; 1 -1 1 -1, ones(1,5)];
b_L = [2 -inf -4]'; % Lower bounds on the linear inequalities
b_U = [inf -2 -2]'; % Upper bounds on the linear inequalities
% Vector m x 1 with observations in objective ||Cx -y(t)||
y = ones(10,1);
% Matrix m x n in objective ||Cx -y(t)||
C = [ ones(1,n); 1 2 1 1 1 1 2 0 0; 1 1 3 1 1 1 -1 -1 -3; ...
1 1 1 4 1 1 1 1 1;1 1 1 3 1 1 1 1 1;1 1 2 1 1 0 0 0 -1; ...
1 1 1 1 0 1 1 1 1;1 1 1 0 1 1 1 1 1;1 1 0 1 1 1 2 2 3; ...
1 0 1 1 1 1 0 2 2];
% Starting point.
x_0 = 1./[1:n]';
% x_min and x_max are only needed if doing plots.
x_min = -ones(n,1);
x_max = ones(n,1);
% x_opt estimate.
x_opt = [2 1.57195927 -1.44540327 -0.03700275 0.54668583 0.17512363 ...
-1.65670447 -0.39474418 0.31002899];
f_opt = 0.1390587318; % Estimated optimum.
% See 'help llsAssign' for more information.
Prob = llsAssign(C, y, x_L, x_U, Name, x_0, ...
[], [], [], ...
A, b_L, b_U, ...
x_min, x_max, f_opt, x_opt);
Result = tomRun('clsSolve', Prob, 1);
%Result = tomRun('nlssol', Prob, 1);
%Result = tomRun('snopt', Prob, 1);
%Result = tomRun('lssol', Prob, 1);