[Couenne] Round function with Couenne package

[Pietro Belotti]

(Same as the reply on the AMPL forum as well)

Suppose we want the variable t[i] to be equal to the ceiling of a variable
x[i]. The ceiling function is indeed not implemented in Couenne, but it
suffices to declare t[i] as integer and then add the two constraints

eps + t[i] >= x[i]
eps + t[i] - 1 <= x[i]

where eps is a small-enough constant, say 1e-5. A nonzero eps allows for
unicity of t[i] (in case x[i] is itself integer), although x[i] 3.000009
will result in t[i] = 3. There are simpler implementations in case you only
require t[i] >= ceil (x[i]) or t[i] <= ceil (x[i]).

Hope this helps,
Pietro

On Sat, Aug 26, 2017 at 6:04 AM, Mahmut Tutam <mtutam at email.uark.edu> wrote:

> Hello,
>
> I am using Couenne open source software with AMPL to solve my
> nonlinear-integer optimization problem. I do not know how to tell AMPL to
> round a function depending on the variable. For example, the following
> function is one of the constraints in my optimization problem such as n is
> variable; and a and nk are parameters. t[i] = round((i * a * n) / (a * (nk
> + 1));. I know I can use ceil function with CPLEX, but CPLEX can not solve
> a nonlinear-integer optimization problem. If I use ceil function in
> Couenne, it says ceil is not implemented. Would you please share me if
> there is a way to deal with this problem? or should I use another software
> package to solve my problem?
>
> Sincerely,
> Mahmut
>
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