Page 310 - MATLAB an introduction with applications

Optimization ——— 295

Optimization terminated: relative infinity-norm of gradient less than
options.TolFun.

x =
0.5000 –1.0000
fval =
3.6609e–016
exitflag =
1
output =
iterations: 8
funcCount: 66
stepsize: 1
firstorderopt: 7.3704e–008
algorithm: ‘medium-scale: Quasi-Newton line search’
message: ‘Optimization terminated: relative infinity-norm of gradient
less than options.TolFun.’

Example E5.16: This is a non-linear inequality constrained example. Find x that solves
2
2
min ( ) x = e 1 x (4x + 2x + 4x x + 2x + 0.9)
f
2
1
1 2
2
x
subject to the constraints
x x – x – x ≤ –2.0
1 2
1
2
x x ≥ –10
1 2
0
Starting guess: x = [–1, 1].
Solution: The constraints are written in the form c(x) ≤ 0.
x x – x – x + 2 ≤ 0
1
2
1 2
–x x – 10 ≤ 0
1 2
MATLAB Solution [Using built-in function]:
Write an m-file objfun.m
function f=objfun(x)
f=exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+0.9);
Write an m-file confun.m for the constraints:
function [c,ceq]=confun(x)
%Nonlinear inequality constraints
c=[2+x(1)*x(2)–x(1)–x(2);–x(1)*x(2)–10];
%Nonlinear inequality constraints
ceq=[];