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

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Valerio Matteucci 2011-9-20

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https://ww2.mathworks.cn/matlabcentral/answers/16292-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