From my understanding, 'lsqnonlin' solves nonlinear least-squares (nonlinear data-fitting) problems.
x = lsqnonlin(fun,x0) starts at the point x0 and finds a minimum of the sum of squares of the functions described in fun.
Here, you have given the initial point as 0.5, and the solution you get is negative, that means, your function (residualFun) sum of squares is minimized at that negative value.
You can try the following format so that the solution is always in the range lb ≤ x ≤ ub,
x = lsqnonlin(fun,x0,lb,ub,options)
where 'lb' and 'ub' are lower and upper bounds respectively.
