MATLAB: Constraining equilibrium solver to positive values (fsolve, lsqnonlin)

fsolvelsqnonlinOptimization Toolbox

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!

Best Answer

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.)
Related Question