Maybe a classical phrase: I have been trying to understand this since several days but not succeed - really about me! Lets take a simple constrained optimization problem from here maximizing revenue with budget constraints. So the problem is
We can solve it in Matlab with fmincon
objective = @(x) -200*x(1)^(2/3)*x(2)^(1/3);
[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = fmincon(objective,[1,1],[],[],[20, 170],20000,[],[],[])
>> X =
666.6669 39.2157
LAMBDA =
struct with fields:
eqlin: 2.5927
OR we can use Lagrangian cost function and rewrite these to unconstrained optimization problem (Am I right at this stage?)
Then solving this objective function with fminsearch or fminunc (even tried with ga)
lambda = 2.5927;
>> objective = @(x) -200*x(1)^(2/3)*x(2)^(1/3)-lambda*(20*x(1) + 170*x(2) - 20000);
x = fminuncfminunc(objective,[1, 1])
>> Problem appears unbounded.
fminunc stopped because the objective function value is less than
or equal to the value of the objective function limit.
<stopping criteria details>
x =
1.0e+19 *
0.2504 6.4423
>> x = fminsearch(objective,[1, 1])
Exiting: Maximum number of function evaluations has been exceeded
- increase MaxFunEvals option.
Current function value: -51855.290146
x =
0.1088 1.7458
gives different results and even not close to constrained solution with fmincon. I tried to change the sign, put lambda = 1....
So why its like this, where I am wrong or I dont understand something?
thanks in advance!