I am looking for a solver that allows me to solve an optimization problem of the form


$$\begin{array}{ll} \text{minimize} & x\_1 x\_2 \cdots x\_n\\ \text{subject to} & \color{gray}{\text{(some linear constraints)}}\end{array}$$


I've used Gurobi before. However, I couldn't find the way to include products in the objective function as well as in the constraints.



Minimizing product subject to linear constraints
This is a hard problem (maximizing the product is a bit better one, as sometimes one can take $\log$ of the objective function, and it becomes concave...). Your best shot might be to use the sum of squares approach for polynomial optimization, as implemented e.g. in [YALMIP](http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Main.WhatIsYALMIP).


