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Optimization problem... closed form solution?

Subject: Optimization problem... closed form solution?
From:
Date: 21 Oct 2006 03:54:44 -0700
Newsgroups: sci.math
Hello,

I am stuck in solving the following problem
z = SIGMA[ (xi-ai)^2 ] + SIGMA[ (yi-bi)^2 ] + [ SIGMA(xi*tanh(yi) +c
]^2
Min(z)

Note that hyperbolic tanget is used, not regular tangent.
i ranges from 1 to n (n is a given number)
ai's and bi's and c are constant
xi's and yi's are (optimization) variables
All variables and constants are real numbers.

Is there any closed form solution for xi's and yi's such that they
minimize z?

Thanks

H.M.


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