Quickguide QP Problem - Revision history

Elias at 11:46, 17 January 2012

2012-01-17T11:46:39Z

← Older revision		Revision as of 07:46, 17 January 2012
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	here <math>c, x, x_L, x_U \in \~~MATHSET~~{R}^n</math>, <math>F \in \~~MATHSET~~{R}^{n		here <math>c, x, x_L, x_U \in \mathbb{R}^n</math>, <math>F \in \mathbb{R}^{n
	\times n}</math>, <math>A \in \~~MATHSET~~{R}^{m_1 \times n}</math>, and <math>b_L,b_U \in		\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>. Equality constraints are defined by setting		\mathbb{R}^{m_1}</math>. Equality constraints are defined by setting
	the lower bound equal to the upper bound, i.e. for constraint <math>i</math>:		the lower bound equal to the upper bound, i.e. for constraint <math>i</math>:
	<math>b_{L}(i) = b_{U}(i)</math>. Fixed variables are handled the same way.		<math>b_{L}(i) = b_{U}(i)</math>. Fixed variables are handled the same way.
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	Open the file for viewing, and execute qpQG in Matlab.		Open the file for viewing, and execute qpQG in Matlab.

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	% qpQG is a small example problem for defining and solving		% qpQG is a small example problem for defining and solving
	% quadratic programming problems using the TOMLAB format.		% quadratic programming problems using the TOMLAB format.
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	%Result = tomRun('knitro', Prob, 1);		%Result = tomRun('knitro', Prob, 1);
	%Result = tomRun('conopt', Prob, 1);		%Result = tomRun('conopt', Prob, 1);
	</~~syntaxhighlight~~>		</source>

Elias at 07:34, 10 August 2011

2011-08-10T07:34:17Z

← Older revision		Revision as of 03:34, 10 August 2011
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			{{Part Of Manual\|title=the Quickguide Manual\|link=[[Quickguide\|Quickguide]]}}
	The general formulation in TOMLAB for a quadratic programming problem is:		The general formulation in TOMLAB for a quadratic programming problem is:

Elias: Created page with "The general formulation in TOMLAB for a quadratic programming problem is: $\begin{array}{ll} \min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x \\ & \\ s/t & \begin{ar..."$

2011-08-10T07:33:49Z

Created page with "The general formulation in TOMLAB for a quadratic programming problem is: <math> \begin{array}{ll} \min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x \\ & \\ s/t & \begin{ar..."

New page

The general formulation in TOMLAB for a quadratic programming problem is:

<math>
\begin{array}{ll}
\min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x \\
& \\
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>

here <math>c, x, x_L, x_U \in \MATHSET{R}^n</math>, <math>F \in \MATHSET{R}^{n
\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>. Equality constraints are defined by setting
the lower bound equal to the upper bound, i.e. for constraint <math>i</math>:
<math>b_{L}(i) = b_{U}(i)</math>. Fixed variables are handled the same way.

Example problem:

The following file defines this problem in TOMLAB.

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

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

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

Name = 'QP Example';
F = [ 8 1 % Matrix F in 1/2 * x' * F * x + c' * x
1 8 ];
c = [ 3 -4 ]'; % Vector c in 1/2 * x' * F * x + c' * x
A = [ 1 1 % Constraint matrix
1 -1 ];
b_L = [-inf 0 ]'; % Lower bounds on the linear constraints
b_U = [ 5 0 ]'; % Upper bounds on the linear constraints
x_L = [ 0 0 ]'; % Lower bounds on the variables
x_U = [ inf inf ]'; % Upper bounds on the variables
x_0 = [ 0 1 ]'; % Starting point
x_min = [-1 -1 ]; % Plot region lower bound parameters
x_max = [ 6 6 ]; % Plot region upper bound parameters

% Assign routine for defining a QP problem.
Prob = qpAssign(F, c, A, b_L, b_U, x_L, x_U, x_0, Name,...
[], [], [], x_min, x_max);

% Calling driver routine tomRun to run the solver.
% The 1 sets the print level after optimization.

Result = tomRun('qpSolve', Prob, 1);
%Result = tomRun('snopt', Prob, 1);
%Result = tomRun('sqopt', Prob, 1);
%Result = tomRun('cplex', Prob, 1);
%Result = tomRun('knitro', Prob, 1);
%Result = tomRun('conopt', Prob, 1);
</syntaxhighlight>

Quickguide QP Problem - Revision history

Elias at 11:46, 17 January 2012

Elias at 07:34, 10 August 2011

Elias: Created page with "The general formulation in TOMLAB for a quadratic programming problem is: \begin{array}{ll} \min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x \\ & \\ s/t & \begin{ar..."

Elias: Created page with "The general formulation in TOMLAB for a quadratic programming problem is: $\begin{array}{ll} \min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x \\ & \\ s/t & \begin{ar..."$