I've designed a cost function of the form
$$ c(x) = \sum_j f_j(x) + \lambda \sum_j g_j(x) $$
which I'm trying to minimize (it's more specifically a non linear least square problem). When I run my algorithm (which is provided by a Matlab toolbox) the final result essentially seems to get stuck in some "local maxima" (when $\lambda$ is high).
More specifically my setup was a relatively high $\lambda$. and some configurations of the $x$ maximize some $f_j$.
I know in general algorithms can get stuck in local minima when minimizing, but I'm surprised an optimization problem can get stuck in local maxima.
Again, is this something that can happen?