I have following optimization problem:
$\max_{u,z} z$
$s.t \quad z - J_i(u,\theta_i) \leq 0 \quad\forall i$
$z$ is a scalar, $J$ is a nonconvex,non linear function of $u$ and $\theta_i$ is just uncertainty ($\theta_i$ shows the $i^{th}$ scenario). So if there are 100 scenarios, there are 100 constraints.
Question is: During iterations, I see $z$ is not monotonically increasing but also decreasing in some steps. Is this something i should expect?
P.S: It is a typical reformulation of $maximin$ objective problem.
Thanks.