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9 QPCON Problem
When solving a problem with a quadratic objective and nonlinear
constraints TOMLAB automatically supplies objective derivatives
(gradient and Hessian) if
qpconAssign is used.
The quadratic constrained nonlinear programming problem is defined
as:
|
|
|
|
| |
|
| s/t |
| xL |
≤ |
x |
≤ |
xU |
| bL |
≤ |
A x |
≤ |
bU |
| cL |
≤ |
c(x) |
≤ |
cU |
|
|
(11) |
where
x,
xL,
xU,
d 
Rn,
F Rn
× n,
f(
x)
R,
A Rm1 ×
n,
bL,
bU Rm1 and
cL,
c(
x),
cU
Rm2.
The following files define and solve an example problem in TOMLAB.
File: tomlab/quickguide/qpconQG.m, qpconQG_c.m, qpconQG_dc.m, qpcon_d2c.m
c: Nonlinear constraint vector
dc: Nonlinear constraint gradient matrix
d2c: The second part of the Hessian to the Lagrangian function for the nonlinear constraints.
The following file illustrates how to solve this QPCON problem in
TOMLAB. Also view the m-files specified above for more information.
File: tomlab/quickguide/qpconQG.m
Open the file for viewing, and execute qpconQG in Matlab.
% qpconQG is a small example problem for defining and solving quadratic
% nonlinearly constrained programming problems using the TOMLAB format.
Name = 'QP constrained problem';
x_0 = ones(10,1);
x_L = [];
x_U = [];
A = ones(8,10);
for i = 1:8
A(i,i) = 1/2;
end
b_L = ones(8,1);
b_U = ones(8,1);
c_L = 4;
c_U = 4;
% Objective f = -x'*x + sum(x), assign as quadratic/linear matrix/vector
F = -2*speye(10);
d = ones(10,1);
Prob = qpconAssign(F, d, x_L, x_U, Name, x_0, A, b_L, b_U,...
'qpconQG_c', 'qpconQG_dc', 'qpconQG_d2c', [], c_L, c_U);
% Run SNOPT as a local solver
Result = tomRun('snopt', Prob, 1);
% Result2 = tomRun('minos', Prob, 1);
% Result3 = tomRun('npsol', Prob, 1);
% Result4 = tomRun('knitro', Prob, 1);
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