Constraining equilibrium solver to positive values (fsolve, lsqnonlin)

From my understanding, it's impossible to constrain fsolve to only find positive zeros but that it is possible using lsqnonlin (see this thread: http://www.mathworks.com/matlabcentral/newsreader/view_thread/280353). I see how I can use bound constraints with lsqnonlin to only return positive values, but how do I "minimize the residuals to 0"? Thank you!

Answer 1

[Andrew Newell]

Suppose you started with a function myfun(x) that inputs a vector x and outputs a vector, for example:

myfun = @(x) x.^2-1;
x0 = [-1.5 1.5];
x1 = fsolve(myfun,x0)

x1 =

   -1.0000    1.0000

To incorporate your constraints, you could do this:

lb = zeros(size(x0)); %lower bound of zero
ub = Inf*ones(size(x0));
x2 = lsqnonlin(myfun,x0,lb,ub)

x2 =

    1.0000    1.0000

As John D'Errico implies, the minimization may give you an answer that is not a root, so you then need to check your answer:

myfun(x2)

ans =

   1.0e-08 *

    0.3056    0.0030

(Note: answer rewritten completely.)

[LS]

Thanks very much for your help!!

Answer 2

[John D'Errico]

There is NO assurance that you can minimize the residuals to zero. What is the root of y=x^2+1, with x restricted to real values?

Just wanting to solve a problem does not mean there will be a solution.