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Avoid discontinuity in optimization problem?

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Dear Friends, I am struggling with an optimization problem and will appreciate any suggestion on it. Following is the description of my problem and I am also attaching the *.nb file to explain it further. Thanks a lot for your help

I have two functions S and X such that:

S is a summation of 30 f[ i, j] functions and X is a function of same 30 f[i, j] functions along with another parameter Ea.

I want to find the optimum (minimum) point for S wrt 30 f[i, j] parameters, such that X is constrained to be zero for different values of Ea (for example from 1E5 - 2E6 with the step size of 1E5) along with other constraints defining the range of values of f[i,j]. On trying NMinimize, I am having following issues –

  1. I am getting a solution for some values of Ea, but for others it comes back with an error message. For which value of Ea error message will appear, is arbitrary and depends upon no of iterations (generally higher no iterations mean lower no of error messages!).
  2. Secondly, when the variation in Ea is continuous, I am expecting the continuous variation in the minimum value of S and f[i,j] values. Due to some strange reason these values are varying abruptly with Ea. Knowing the physical model, if I intuit the values of f[i, j], those obtained for Ea = 2E6 seems reasonable and should decrease continuously with decreasing Ea, which is not the case.
Attachments:
POSTED BY: S G
Answer
6 months ago

NMinimize searches for the global optimum but does not necessarily find it. That may be the reason for the abrupt variation that you are puzzled about.

POSTED BY: Frank Kampas
Answer
6 months ago

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