Elias at 22:17, 17 January 2012

2012-01-17T22:17:22Z

← Older revision		Revision as of 17:17, 17 January 2012
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	<math>		<math>
	\begin{array}{cccccc} \min\limits_x & ~~\multicolumn{5}{l}~~{\max \ \ lam: r(x) - w * lam \leq g} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\ {} & c_L & \leq & c(x) & \leq & c_U \\\end{array}		\begin{array}{cccccc} \min\limits_x & {\max \ \ lam: r(x) - w * lam \leq g} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\ {} & c_L & \leq & c(x) & \leq & c_U \\\end{array}
	</math>		</math>

	where <math>x,x_L,x_U \in R^{n}</math>, <math>r(x) \in R^{N}</math>, <math>c(x),c_L,c_U		where <math>x,x_L,x_U \in \mathbb{R}^{n}</math>, <math>r(x) \in \mathbb{R}^{N}</math>, <math>c(x),c_L,c_U
	\in R^{m_1}</math>, <math>b_L,b_U \in R^{m_2}</math>, <math>A\in R^{m_2 \times		\in \mathbb{R}^{m_1}</math>, <math>b_L,b_U \in \mathbb{R}^{m_2}</math>, <math>A\in \mathbb{R}^{m_2 \times
	n}</math>, <math>g \in R^{m}</math>, and <math>w \in R^{m}</math>.		n}</math>, <math>g \in \mathbb{R}^{m}</math>, and <math>w \in \mathbb{R}^{m}</math>.

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

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	% goalsQG is a small example problem for defining and solving		% goalsQG is a small example problem for defining and solving
	% multi criteria optimization problems using the TOMLAB format.		% multi criteria optimization problems using the TOMLAB format.
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	PriLev = 2;		PriLev = 2;
	Result = tomRun('goalSolve', Prob, PriLev);		Result = tomRun('goalSolve', Prob, PriLev);
	</~~syntaxhighlight~~>		</source>

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained goal attainment''' ('''goal''') problem is defined as $\begin{array}{cccc..."$

2011-08-10T13:48:11Z

Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained goal attainment''' ('''goal''') problem is defined as <math> \begin{array}{cccc..."

New page

{{Part Of Manual|title=the Quickguide Manual|link=[[Quickguide|Quickguide]]}}
The '''constrained goal attainment''' ('''goal''') problem is defined as

<math>
\begin{array}{cccccc} \min\limits_x & \multicolumn{5}{l}{\max \ \ lam: r(x) - w * lam \leq g} \\ \mbox{subject to} & x_L & \leq & x & \leq & x_U \\ {} & b_L & \leq & Ax & \leq & b_U \\ {} & c_L & \leq & c(x) & \leq & c_U \\\end{array}
</math>

where <math>x,x_L,x_U \in R^{n}</math>, <math>r(x) \in R^{N}</math>, <math>c(x),c_L,c_U
\in R^{m_1}</math>, <math>b_L,b_U \in R^{m_2}</math>, <math>A\in R^{m_2 \times
n}</math>, <math>g \in R^{m}</math>, and <math>w \in R^{m}</math>.

The goal solution can be obtained by the use of any suitable nonlinear TOMLAB solver.

The following files define a problem in TOMLAB.

'''File: '''tomlab/quickguide/goalsQG_r.m, goalsQG_J.m, goalsQG_c, goalsQG_dc

<pre>
r: Residual vector
J: Jacobian matrix
c: Nonlinear constraint vector
dc: Nonlinear constraint gradient matrix
</pre>

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

'''File: '''tomlab/quickguide/goalsQG.m

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

<syntaxhighlight lang="matlab">
% goalsQG is a small example problem for defining and solving
% multi criteria optimization problems using the TOMLAB format.

Name='EASY-TP355';
% Constrained least squares problem, four quadratic terms and local solutions
% Hock W., Schittkowski K. (1981):
x_0 = zeros(4,1); % Lower bounds for x.
x_L = zeros(4,1); % Upper bounds for x.
x_U = 1e5*ones(4,1); % Starting point.
x_min = []; % For plotting.
x_max = []; % For plotting.
A = [1 0 0 0;0 1 0 0]; % Linear constraints.
b_L = [0.1;0.1]; % Lower bounds.
b_U = [0.1;0.1]; % Upper bounds.
c_L = 0; % Lower bounds.
c_U = 0; % Upper bounds.
y = zeros(2,1); % Residuals

Prob = clsAssign('goalsQG_r', 'goalsQG_J', [], x_L, x_U, Name, x_0,...
y, [], [], [], [], [],...
A, b_L, b_U, 'goalsQG_c', 'goalsQG_dc', [], c_L, c_U,...
x_min, x_max);

PriLev = 2;
Result = tomRun('goalSolve', Prob, PriLev);
</syntaxhighlight>

Quickguide GOAL Problem - Revision history

Elias at 22:17, 17 January 2012

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained goal attainment''' ('''goal''') problem is defined as \begin{array}{cccc..."

Elias: Created page with "{{Part Of Manual|title=the Quickguide Manual|link=Quickguide}} The '''constrained goal attainment''' ('''goal''') problem is defined as $\begin{array}{cccc..."$