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FindMaximum causes kernel to quit (no more memory) at 20 variables

Posted 2 months ago
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I basically have FindMaximum[{F,cons},z], with F[z] the highest real part of the eigenvalues of a matrix, cons are constraints, and z is a list of variables. It works great up until 20 variables, but I need to go much higher. Any ideas?

Notebook attached. The loop is artificially set for only ii=3, for which there is no problem. When you set ii=6, it hangs up on memory (at least for me using my laptop and version 8 of Mathematica)

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