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23 GOAL Problem
The
constrained goal attainment (
goal) problem is
defined as
|
|
max lam: r(x) − w * lam ≤ g |
subject to |
xL |
≤ |
x |
≤ |
xU |
|
bL |
≤ |
Ax |
≤ |
bU |
|
cL |
≤ |
c(x) |
≤ |
cU |
|
(25) |
where
x,
xL,
xU Rn,
r(
x)
RN,
c(
x),
cL,
cU
Rm1,
bL,
bU Rm2,
A Rm2 ×
n,
g Rm, and
w Rm.
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);
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