Quickguide LPCON Problem - Revision history

Elias at 11:49, 17 January 2012

2012-01-17T11:49:16Z

← Older revision		Revision as of 07:49, 17 January 2012
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	where <math>x, x_L, x_U, d \in \~~MATHSET~~{R}^n</math>, <math>f(x) \in \~~MATHSET~~{R}</math>, <math>A		where <math>x, x_L, x_U, d \in \mathbb{R}^n</math>, <math>f(x) \in \mathbb{R}</math>, <math>A
	\in \~~MATHSET~~{R}^{m_1 \times n}</math>, <math>b_L,b_U \in \~~MATHSET~~{R}^{m_1}</math> and		\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 \~~MATHSET~~{R}^{m_2}</math>.		<math>c_L,c(x),c_U \in \mathbb{R}^{m_2}</math>.

	The following files define an example problem in TOMLAB.		The following files define an example problem in TOMLAB.
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	Open the file for viewing, and execute lpconQG in Matlab.		Open the file for viewing, and execute lpconQG in Matlab.

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	% lpconQG is a small example problem for defining and solving linear		% lpconQG is a small example problem for defining and solving linear
	% nonlinearly constrained programming problems using the TOMLAB format.		% nonlinearly constrained programming problems using the TOMLAB format.
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	% Prob.KNITRO.options.ALG = 3;		% Prob.KNITRO.options.ALG = 3;
	% Result3 = tomRun('knitro', Prob, 1);		% Result3 = tomRun('knitro', Prob, 1);
	</~~syntaxhighlight~~>		</source>

Elias at 08:26, 10 August 2011

2011-08-10T08:26:28Z

← Older revision		Revision as of 04:26, 10 August 2011
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			{{Part Of Manual\|title=the Quickguide Manual\|link=[[Quickguide\|Quickguide]]}}
	When solving a problem with a linear objective and nonlinear constraints there is no need to explicitly code the gradient or Hessian. TOMLAB automatically supplies these if ''lpconAssign'' is used.		When solving a problem with a linear objective and nonlinear constraints there is no need to explicitly code the gradient or Hessian. TOMLAB automatically supplies these if ''lpconAssign'' is used.

Elias: Created page with "When solving a problem with a linear objective and nonlinear constraints there is no need to explicitly code the gradient or Hessian. TOMLAB automatically supplies these if ''lpc..."

2011-08-10T08:20:55Z

Created page with "When solving a problem with a linear objective and nonlinear constraints there is no need to explicitly code the gradient or Hessian. TOMLAB automatically supplies these if ''lpc..."

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When solving a problem with a linear objective and nonlinear constraints there is no need to explicitly code the gradient or Hessian. TOMLAB automatically supplies these if ''lpconAssign'' is used.

The linear constrained nonlinear programming problem is defined as:

<math>
\begin{array}{ll}
\min\limits_{x} & f(x) = d^T 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, d \in \MATHSET{R}^n</math>, <math>f(x) \in \MATHSET{R}</math>, <math>A
\in \MATHSET{R}^{m_1 \times n}</math>, <math>b_L,b_U \in \MATHSET{R}^{m_1}</math> and
<math>c_L,c(x),c_U \in \MATHSET{R}^{m_2}</math>.

The following files define an example problem in TOMLAB.

'''File: '''<span class="roman">tomlab/quickguide/lpconQG.m, lpconQG_c.m, lpconQG_dc.m, lpcon_d2c.m</span>

<pre>
c: Nonlinear constraint vector
dc: Nonlinear constraint gradient matrix
d2c: The second part of the Hessian to the Lagrangian function for the nonlinear constraints.
</pre>

The following file illustrates how to solve this LPCON problem in TOMLAB. Also view the m-files specified above for more information.

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

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

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

Name = 'Linear constrained problem';
A = [1 0 -1 0
0 1 0 -1
0 0 1 -1];
b_L = [1 1 0]';
b_U = [];
c_L = -1;
c_U = -1;

x_0 = [1 1 1 1]'; % Starting value (not used)

x_L = [-Inf -Inf -Inf 1]'; % Lower bounds for x
x_U = 100*ones(4,1); % Upper bounds for x

% Objective f = 3*x(1)+2*x(2), assign as linear vector

d = [3 2 0 0]';

Prob = lpconAssign(d, x_L, x_U, Name, x_0, A, b_L, b_U,...
'lpconQG_c', 'lpconQG_dc', 'lpconQG_d2c', [], c_L, c_U);

% Run a global solver for 10000 function evaluations.
Result = tomRun('glcFast', Prob, 1);

% Assign new starting point.
Prob.x_0 = Result.x_k(:,1);

% Run SNOPT as a local solver.

Result2 = tomRun('snopt', Prob, 1);

% Try KNITRO as a local solver, ALG = 3
% Prob.KNITRO.options.ALG = 3;
% Result3 = tomRun('knitro', Prob, 1);
</syntaxhighlight>