sci.op-research

I have a problem with mixed integer-valued and real-valued decision
variables. The problem has a wide variety of constraints, but all are
linear. The objective function is composed of a subset of the
decision variables and can be expressed as the sum of products of
these variables:

Minimize Sum_i ( Product_j x_i_j)

Here "Sum_i" denotes the summation over the index "i." All the
decision variables in the objective function are real-valued and
between 0 and 1. I tried to use a piecewise linear approximation
(exponentiating the log of the product) for the objective function,
but that won't work. I won't explain why, but I expect that this
won't surprise anyone.

I know this is a nonlinear programming problem, but I'm hoping that
someone has experience with this kind of nonlinear program. I know
that the objective function is a posynomial, but that's the extent of
my nonlinear programming knowledge. I'd appreciate any advice, any
suggested references, or just gut feelings for solving such a problem
to optimality.

If I can't find a way soon, I'll have to make use of one or more
heuristic methods (GA, Simulated Annealing, Tabu, GRASP, etc.). I'd
also appreciate any thoughts on heuristic methods for such problems.
Thanks in advance for any help.