Page 311 - MATLAB an introduction with applications

296 ——— MATLAB: An Introduction with Applications

Invoke constrained optimization routine:
>> x0=[–1,1]; % Initial guess at the solution
>> options=optimset(‘LargeScale’, ‘off’);
>> [x,fval]=fmincon(@objfun,x0,[],[],[],[],[],[],@confun,options)
Optimization terminated: first-order optimality measure less
than options.TolFun and maximum constraint violation is less
than options.TolCon.
Active inequalities (to within options.TolCon = 1e–006):
lower upper ineqlin ineqnonlin
1
2
x =
–9.5474 1.0474
fval =
0.0236
>> [c,ceq]=confun(x)
c =
1.0e–007 *
–0.9035
0.9035
ceq =
[]
Example E5.17: This is a constrained optimization example: inequalities and bounds.
2
2
x
Minimize f () = e 1 x (4x + 2x + 4x x + 2x + 0.9)
2
1
1 2
2
subject to 2 + x x – x – x ≤ 0
1 2
1
2
–x x ≤ 0
1 2
x ≥ 0
1
x ≥ 0
2
0
Initial values: x = [–1, 1].
Solution:
MATLAB Solution [Using built-in function]:
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);
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=[];