Originally posted by: hzy_cims

Could contraints contains Hyperbolic functions, such as y=tanh(x), in Cplex?
My optimization problem has connection with neural network theory, so certainly can not avoid of involving the Hyperbolic functions. And I don't know whether cplex could express that functions.
If anyone have suggestions or ideas, please let me know, thank you!
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Originally posted by: SystemAdmin

No. CPLEX is limited to linear or quadratic constraints and objectives.

Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
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Originally posted by: EdKlotz

> Paul Rubin wrote:
> No. CPLEX is limited to linear or quadratic constraints and objectives.
>
> Paul
>
> Mathematicians are like Frenchmen: whenever you say something to them, they
> translate it into their own language, and at once it is something entirely
> different. (Goethe)

CPLEX also supports second order cone constraints, which is how it solves
problems with convex quadratic constraints (i.e. it transforms those constraints into second order cone constraints). And, there are a surprisingly larger number
of nonquadratic but convex nonlinear functions that can be transformed into second
order cone problems that CPLEX can solve. For example, minimizing the hyperbolic function 1/x for x > 0 can be reformulated as

min u
s.t.
v = x
1 <= uv
u >= 0
x >= eps

The constraint uv >= 1 is a rotated second order cone constraint that CPLEX
can process. See the user manual on second order cones for more information.

The above example is a special case of a more general example described in
the paper Second Order Cone Programming by Alizadeh and Goldfarb. That paper
contains several other examples of seemingly hopelessly nonlinear functions
that not only are convex, but can be reformulated as SOCPs, and therefore
solved by CPLEX.

Now, tanh(x) is not convex or concave. However, it is convex for negative
values and convex for positive values of x. So, if your application only
looks at one of those domains, perhaps there is some transformation or hyperbolic
approximation function you can use to turn it into an SOCP and solve it using
CPLEX. Otherwise, the only way you could solve this using CPLEX involves using
a piecewise linear approximation of this nonconvex function and solving the resulting MIP.
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Originally posted by: FiFila

Hi;

I want to model by CP optimizer and NN a problem (I want to improve the NN by combination of it with constraint programming). As the input of NN is not linear, I can not use CPLEX, I have force to use a CP optimizer. Because I am in primary steps of learning a CP optimizer, would you please send me a sample or reference to see how I can model some constraints by CP optimizer as  a nonlinear input of  my NN.

 

 

Another question: Is it possible to write the neural network section in Matlab and its constraints section in CPLEX?

Thanks

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You should start a new thread for these questions since they seem rather unrelated to this 4 year old thread.

For CP related questions you should refer to the CP optimizer forum.

It is possible to invoke CPLEX from matlab, see here. Whether this allows you to combine matlab's neural network features with CPLEX I cannot tell.

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