function approximation using any optimization routine

2017 6 21
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更新时间：2017 6 23
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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!

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Walter Roberson
Walter Roberson 2017-6-21

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

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ARUN BORGOHAIN
ARUN BORGOHAIN 2017-6-21
Thanks; I had mistaken by taken -ve sign instead +ve in bet. the two equations!
Walter Roberson
Walter Roberson 2017-6-21
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
ARUN BORGOHAIN 2017-6-22
编辑：Walter Roberson 2017-6-22
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
Walter Roberson 2017-6-22
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
ARUN BORGOHAIN 2017-6-22
编辑：ARUN BORGOHAIN 2017-6-23
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!

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