There is a function in Matlab called "fmincon()". Currently, I need to solve a lagrange multiplier problem which can be solved by fmincon() function. However, the number of constrain is quite high and the constrains are nonlinear. The problem looks like this:
$\min _{c^{\prime}}\left\|c^{\prime}-c\right\|^{2}$
s.t. $\left\|x_{i}-c\right\|^{2} \leqslant d_{i},$ $1 \leqslant i \leqslant n$
In which the vector $c$, $x_{i}$ and the scalar $d_{i}$ are given, and I want to find $c^{\prime}$.
Now, the number of constrains $n$ may be quite large. I am wondering the computational complexity of that function regarding to the number and the complexity of constrains. Or just the time complexity of solving a lagrange multiplier problem.