function approximation using any optimization routine

I've two linear equs: x1+x2=10 & x1-x2=2;

I would like to solve these using any optimization method for which these have to convert into a single function; In excel:i am doing this by excel solver by minimising sum sq deviation (initially assuming any values for x1 & x2); pl. help how to do it in matlab! Ex: I try to apply ga; but fail to make the needed fitness function!

Answer 1

[Walter Roberson]

fun = @(x) (x(1)+x(2)-10).^2 + (x(1)-x(2)-2).^2

[ARUN BORGOHAIN]

Thanks; I had mistaken by taken -ve sign instead +ve in bet. the two equations!

[Walter Roberson]

The general form is ((lhs) - (rhs)).^2 where lhs is left hand side and rhs is right hand side; you calculate that for each equation and then add them together.

[ARUN BORGOHAIN]

Instead of writing equations::if I make A&b matrix data, how to call these(say):

fun=@(x)(sum(A*x-b).^2);

I guess have to use loop for indexing A,b&x? if i get some guidance!

In one of your answer I got a similar type:

@(x)A*x.'-b    % x.' ?

res = @(x)sum(fun(x).^2); 

X = fmincon(res,x0);

[Walter Roberson]

Yes, looks good. You might find you need @(x)A*x-b instead of @(x)A*x.'-b but one of the two should work.

[ARUN BORGOHAIN]

Thanks! when using fsolve

fun=@(x)A*x-b % is ok

but ga works as

fun=@(x)sum (A*x'-b).^2

Maths is really an obsession; I am 50+ but pass my lots of time in maths; these days R is also equally informative! I've seen vdo in matlab site where even 70+ resource personalities also giving demos/taking classes::it might be challenging to keep a pace with all topics of maths! For ex: I donot like fuzzy&markov! thanks once again!