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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.

Mohsin
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  • Impossible to answer unless you tell us how you solve the problem. – Johan Löfberg Feb 20 '15 at 16:04
  • I use KNITRO as an optimization solver with interior point method. It is a black box solver for me. So i can't tell more either. – Mohsin Feb 20 '15 at 16:09
  • Not too strange. An infeasible method is probably used, so on the way towards feasibility, optimality could decrease at some points to improve feasibility – Johan Löfberg Feb 20 '15 at 16:43

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