genetic algorithm (ga) + fmincon in an application of Vasicek model problem.

hi, i would apologize for my bad english.

My problem consist in finding the minimum in 5 variables of a 6 variables function, that rapresents the term structure of interest rates in the Vasicek model, with a nice approx.

I decided to apply GA to find a nice start point for fmincon (I use fmincon because I need to introduce constraints, the variables must be positive.)

function def: (R(0,Ti))

      function f = sttdi(x)

      %x(1)= gamma ; x(2)= rho ; x(3)= alfa ; x(4)= r0 ; x(5)= q  

      T=4;

      f = x(1)+((x(2)*x(5))/x(3))-((1/2)*((x(2)^2)/x(3)))+(x(4)-(x(1)+((x(2)*x(5)/x(3))-((1/2)*((x(2)^2)/x(3))))))*(1/(x(3)*T))*(1-(exp(-x(3)*T)))+(x(2)^2/4*x(3)^3*T)*((1-(exp(-x(3)*T)))^2);

A = [-1 0 0 0 0  ; 0 -1 0 0 0  ; 0 0 -1 0 0  ; 0 0 0 -1 0  ; 0 0 0 0 -1 ];  

b = [0 0 0 0 0 ];

Now from command window :

>> x=ga(@rel1,5,A,b)

Optimization terminated: maximum number of generations exceeded.

x =

      3.0140    8.4916    0.0000    1.3246    9.5596

>> options=optimset('Algorithm', 'sqp')

>> [x,fval]=fmincon(@rel1,x,A,b,[],[],[],[],[],options)

Problem appears unbounded.

fmincon stopped because the objective function value is less than
the default value of the objective function limit and constraints 
are satisfied to within the default value of the constraint tolerance.

<stopping criteria details>

x =

    1.0e+013 *

      0.0000    0.4439    0.0000    0.0000    3.5294

fval =

   -6.3969e+040

I can not understand the output, as can be x (3) = 0 if it appears in the denominator? I'm doing the conceptual errors?

Thanks guys

Answer 1

[Walter Roberson]

Before you run the problem, command

format long g

and then run it.

You will likely see that your x values are non-zero.

Answer 2

[Valerio Matteucci]

fmincon solution should not be at least close to that found by genetic algorithm?