Elias at 11:50, 17 January 2012

2012-01-17T11:50:47Z

← Older revision		Revision as of 06:50, 17 January 2012
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	where <math>x, x_L, x_U \in \~~MATHSET~~{R}^n</math>, <math>d \in \~~MATHSET~~{R}^M</math>, <math>C \in		where <math>x, x_L, x_U \in \mathbb{R}^n</math>, <math>d \in \mathbb{R}^M</math>, <math>C \in
	\~~MATHSET~~{R}^{M \times n}</math>, <math>A \in \~~MATHSET~~{R}^{m_1 \times n}</math> and		\mathbb{R}^{M \times n}</math>, <math>A \in \mathbb{R}^{m_1 \times n}</math> and
	<math>b_L,b_U \in \~~MATHSET~~{R}^{m_1}</math>. The variables <math>x \in I</math>, the index		<math>b_L,b_U \in \mathbb{R}^{m_1}</math>. The variables <math>x \in I</math>, the index
	subset of <math>1,...,n</math>, are restricted to be integers.		subset of <math>1,...,n</math>, are restricted to be integers.

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	Open the file for viewing, and execute millsQG in Matlab.		Open the file for viewing, and execute millsQG in Matlab.

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	% millsQG is a small example problem for defining and solving		% millsQG is a small example problem for defining and solving
	% mixed-integer linear least squares using the TOMLAB format.		% mixed-integer linear least squares using the TOMLAB format.
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	Result = tomRun('cplex', Prob, 1);		Result = tomRun('cplex', Prob, 1);
	% Result = tomRun('minlpBB', Prob, 1);		% Result = tomRun('minlpBB', Prob, 1);
	</~~syntaxhighlight~~>		</source>

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''mixed-integer linear least squares''' ('''mills''') problem is defined as $\begin{..."$

2011-08-10T08:47:42Z

Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''mixed-integer linear least squares''' ('''mills''') problem is defined as <math> \begin{..."

New page

{{Part Of Manual|title=the Quickguide Manual|link=[[Quickguide|Quickguide]]}}
The '''mixed-integer linear least squares''' ('''mills''') problem is defined as

<math>
\begin{array}{ll}
\min\limits_{x} & f(x) = \frac{1}{2} || C x - d || \\
& \\
s/t & \begin{array}{lcccl}
x_{L} & \leq & x & \leq & x_{U}, \\
b_{L} & \leq & A x & \leq & b_{U} \\
\end{array}
\end{array}
</math>

where <math>x, x_L, x_U \in \MATHSET{R}^n</math>, <math>d \in \MATHSET{R}^M</math>, <math>C \in
\MATHSET{R}^{M \times n}</math>, <math>A \in \MATHSET{R}^{m_1 \times n}</math> and
<math>b_L,b_U \in \MATHSET{R}^{m_1}</math>. The variables <math>x \in I</math>, the index
subset of <math>1,...,n</math>, are restricted to be integers.

The following file defines and solves a problem in TOMLAB.

'''File: '''<span class="roman">tomlab/quickguide/millsQG.m</span>

Open the file for viewing, and execute millsQG in Matlab.

<syntaxhighlight lang="matlab">
% millsQG is a small example problem for defining and solving
% mixed-integer linear least squares using the TOMLAB format.
Name='MILLS test example'; % Problem name, not required.
n = 10;
x_L = zeros(n,1); % Lower bounds on x
x_U = 20*ones(n,1); % Upper bounds on x

% Matrix defining linear constraints
A = [ ones(1,n) ; 1:10; -2 1 -1 1 -1 1 -1 1 -1 1];
b_L = [35 -inf 29]'; % Lower bounds on the linear inequalities
b_U = [inf 120 210]'; % Upper bounds on the linear inequalities

% Vector m x 1 with observations in objective ||Cx -y(t)||
y = 2.5*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 0; 1 1 3 1 1 1 -1 -1 -3 1; ...
1 1 1 4 1 1 1 1 1 0;1 1 1 3 1 1 1 1 1 0;1 1 2 1 1 0 0 0 -1 1; ...
1 1 1 1 0 1 1 1 1 0;1 1 1 0 1 1 1 1 1 1;1 1 0 1 1 1 2 2 3 0; ...
1 0 1 1 1 1 0 2 2 1];

% 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);

% See 'help llsAssign' for more information.
Prob = llsAssign(C, y, x_L, x_U, Name, x_0, ...
[], [], [], ...
A, b_L, b_U);

IntVars = logical([ones(n-2,1);zeros(2,1)]);

Prob = lls2qp(Prob, IntVars);

Result = tomRun('cplex', Prob, 1);
% Result = tomRun('minlpBB', Prob, 1);
</syntaxhighlight>

Quickguide MILLS Problem - Revision history

Elias at 11:50, 17 January 2012

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''mixed-integer linear least squares''' ('''mills''') problem is defined as \begin{..."

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''mixed-integer linear least squares''' ('''mills''') problem is defined as $\begin{..."$