Page 314 - MATLAB an introduction with applications

Optimization ——— 299

Solution:
MATLAB Solution [Using built-in function]:
The objective function nd its gradient re-defined in the m-file objfun.m as follows:

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);
The m-file confuneq.m contains the equality and inequality constraints:
function [c,ceq]=confuneq(x)
c=–x(1)*x(2)–10;
ceq=x(1)^2+x(2)–1;
Define a guess at the solution:
>> x0=[–1,1];
We will use the option as below:
>> options=optimset(‘LargeScale’, ‘off’);
Call the optimization algorithm:
>> [x,fval,exitflag,output]=fmincon(@objfun,x0,[],[],[],[],[],[],@confuneq,
options);
Optimization terminated: first-order optimality measure less than options.
TolFun
and maximum constraint violation is less than options.TolCon.
No active inequalities.
>> x
x =
–0.7488 0.4393
The function value at the solution is
>> fval
fval =
1.4621

The constraint values at the solution are
>> [c,ceq]=confuneq(x)

c =
–9.6710
ceq =
6.4376e–009
The total number of function evaluations was
>> output.funcCount
ans =
21
Changing the default termination tolerances