Have there been attempts to factor integers with Linear Programming?
Searching the internet suggests that for Integer Factorization only Number Theoretic algorithms, like sieves, are taken into consideration. On the other hand, Linear Programming is successfully applied to a variety of combinatorial problems, so that should be motivation enough to try to make it also applicable to Integer Factorization.
I have managed to find such a formulation and I would like references to literature, where such formulations and their discussion from the practical and theoretical point of view can be found.
in view of the feedback I have received, I would like to point out, that the emphasis is on Linear Integer Programming or Linear Programming formulations of the Integer Factorization Problem;
as a motivation, the fact that ILP is fixed parameter tractable and this publication http://e-ntrasites.univpm.it/Ingegneria/Engine/RAServeFile.php/f/Angelo_Parente.pdf should suffice.
The "steam hammer" of general Integer Programming that solves every NP problem, is too heavy weight and references to related publications are not desirable to me.
references that are related to the question whether Integer Factorization is in $PTAS$ or $APX$ or any other complexity class, are also welcome.
references related to the question whether the integrality gap of the $LP$ formulation of Integer Factorization is small enough to allow cryptographic attacks, are welcome, too.