Elias at 22:15, 17 January 2012

2012-01-17T22:15:50Z

← Older revision		Revision as of 17:15, 17 January 2012
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	<math>		<math>
	\begin{array}{cccccc} \min\limits_x & ~~\multicolumn{5}{l}~~{c1 x \over c2 x} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\\end{array}		\begin{array}{cccccc} \min\limits_x & {c1 x \over c2 x} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\\end{array}
	</math>		</math>

	where <math>c1,c2,x,x_L,x_U \in \~~Rdim~~{n}</math>, <math>b_L,b_U \in \~~Rdim~~{m_2}</math>, and		where <math>c1,c2,x,x_L,x_U \in \mathbb{R}^{n}</math>, <math>b_L,b_U \in \mathbb{R}^{m_2}</math>, and
	<math>A\in \~~Rdim~~{m_1 \times n}</math>.		<math>A\in \mathbb{R}^{m_1 \times n}</math>.

	The LINRAT solution can be obtained by the use of any suitable linear <span class="roman">TOMLAB</span> solver.		The LINRAT solution can be obtained by the use of any suitable linear <span class="roman">TOMLAB</span> solver.
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	Open the file for viewing, and execute linratQG in Matlab.		Open the file for viewing, and execute linratQG in Matlab.

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	% linratQG is a small example problem for defining and solving		% linratQG is a small example problem for defining and solving
	% linear ratio programming problems using the TOMLAB format.		% linear ratio programming problems using the TOMLAB format.
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	Result = tomRun('linRatSolve', Prob, PriLev);		Result = tomRun('linRatSolve', Prob, PriLev);
	</~~syntaxhighlight~~>		</source>

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The linearly '''constrained linear ratio''' ('''LINRAT''') problem is defined as $\begin{arr..."$

2011-08-10T13:42:16Z

Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The linearly '''constrained linear ratio''' ('''LINRAT''') problem is defined as <math> \begin{arr..."

New page

{{Part Of Manual|title=the Quickguide Manual|link=[[Quickguide|Quickguide]]}}
The linearly '''constrained linear ratio''' ('''LINRAT''') problem is defined as

<math>
\begin{array}{cccccc} \min\limits_x & \multicolumn{5}{l}{c1 x \over c2 x} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\\end{array}
</math>

where <math>c1,c2,x,x_L,x_U \in \Rdim{n}</math>, <math>b_L,b_U \in \Rdim{m_2}</math>, and
<math>A\in \Rdim{m_1 \times n}</math>.

The LINRAT solution can be obtained by the use of any suitable linear <span class="roman">TOMLAB</span> solver.

The following file illustrates how to solve a LINRAT problem in TOMLAB.

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

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

<syntaxhighlight lang="matlab">
% linratQG is a small example problem for defining and solving
% linear ratio programming problems using the TOMLAB format.

Name = 'Linear Ratio 1';
x_0 = [2;2;2;2]; % Initial value
x_L = [1;2;3;4]; % Lower bounds on x
x_U = [100;100;50;50]; % Upper bounds on x

% Define the numerator and denominator for the objective
c1 = [3;7;9;11];
c2 = [20;15;10;5];

% Add the linear constraint x(1) + x(2) + x(3) + x(4) - 20 <= 0
% Write the constraint as x(1) + x(2) + x(3) + x(4) <= 20

% The A matrix could be specified dense or sparse
% A = sparse([1 1 1 1]);

A = [1 1 1 1];
b_L = -inf;
b_U = 20;

c = zeros(4,1); % Dummy objective

% Generate an LP problem using the Tomlab Quick format
% Use mipAssign if solving a mixed-integer problem
Prob = lpAssign(c, A, b_L, b_U, x_L, x_U, x_0, Name);
Prob.QP.c1 = c1;
Prob.QP.c2 = c2;

Prob.SolverRat = 'minos';

% One may set other solvers:
% Prob.SolverRat = 'cplex';
% Prob.SolverRat = 'xa';
% Prob.SolverRat = 'snopt';
% Prob.SolverRat = 'milpSolve';

% Set print level 1 to get output from PrintResult at the end
PriLev = 1;
Prob.PriLevOpt = 0;

Result = tomRun('linRatSolve', Prob, PriLev);
</syntaxhighlight>

Quickguide LINRAT Problem - Revision history

Elias at 22:15, 17 January 2012

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The linearly '''constrained linear ratio''' ('''LINRAT''') problem is defined as \begin{arr..."

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The linearly '''constrained linear ratio''' ('''LINRAT''') problem is defined as $\begin{arr..."$