Im currently implementing a Nelder-Mead algorithm in MATLAB that can deal with constraints. In detail, the constraints should be added to the objective function with a Lagrange Multiplier($\lambda$) and the new function is then minimized by Nelder-Mead. Looks something like this.
$$L(x_1, \ldots,x_n,\lambda_1, \ldots,\lambda_n) = f(x_1,\ldots,x_n)+ \lambda\left(c-g(x_1,\ldots,x_n)\right)$$
this works for constraints that are equations, $g(x_1,\dots,x_n)= c$
How does it work with constraints that are upper and lower bounds? cant put them into the objective function like that
Are the multipliers to be treated as additional variables by the nelder mead or are they constants you need to set?
Thank you guys.