Minimum of function by vector parameters

[EDIT: Fri May 13 15:01:56 UTC 2011 - Clarify - MKF]

Hello

I'd like to find the minimum of the following function

function y=probability_financial(a,b,w,pm,z)
% w=[w1,w2]
% a=[a1 a2] 
% b=[b1 b2];
% z-matrix (2x2) is defined, 
% pm = [pm1, pm2]-vector, is defined

y = abs(pm(1)-w(1)/(1+exp(-a(1)-b(1)*z(1,1)))-w(2)/...
    (1+exp(-a(2)-b(2)*z(1,2))))+abs(pm(2)-w(1)/...
    (1+exp(-a(1)-b(1)*z(2,1)))-w(2)/(1+exp(-a(2)-b(2)*z(2,2))));
end

by the following variables w=[w1,w2], a=[a1 a2] b=[b1 b2]

Would you be so kind to explain to me how to implement this?

Thanks for your answers!

[Andrew Newell]

Do you have the Optimization Toolbox?

Answer 1

[Walter Roberson]

As you have an excess of unconstrained free variables, you can make some arbitrary choices and minimize exactly at those choices.

For example, Let

w(2) = 0
a(1) = arbitrary real value (does affect other variables)
a(2) = any real value (contribution will be ignored)
b(2) = any real value (contribution will be ignored)

Then

w(1) = pm(1)*exp((-a(1)*z(1,1)+a(1)*z(1,2)+ln(pm(2)/pm(1))*z(1,1))/(z(1,1)-z(1,2)))

b(1) = -ln(pm(2)/pm(1))/(z(1,1)-z(1,2))

will minimize to y = 0