Quickguide GOAL Problem: Difference between revisions
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(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...") |
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<math> | <math> | ||
\begin{array}{cccccc} \min\limits_x & | \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. | ||
< | <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); | ||
</ | </source> | ||
Latest revision as of 18:17, 17 January 2012
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This page is part of the Quickguide Manual. See Quickguide. |
The constrained goal attainment (goal) problem is defined as
where , , , , , , and .
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
r: Residual vector J: Jacobian matrix c: Nonlinear constraint vector dc: Nonlinear constraint gradient matrix
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.
% 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);