I have a nonconvex optimization problem with a linear objective function, a set of linear constraints and a set of nonlinear, nonconvex constraints. Is this problem NPhard? If so, how can I prove this?

$\begingroup$ As @Brian Borchers says in his answer, this is impossible to answer without seeing the problem. $\endgroup$ – Igor Rivin Jul 5 '13 at 3:35
In general, you can show that a class of problems is NPHard by taking a known NPhard problem and reducing it to a problem in your class (being careful that size of the problem does not increase too much.)
Since some well known NPhard problems can easily be rewritten as nonlinear optimization problems with nonconvex constraints, the class of nonconvex nonlinear optimization problems is in general NPHard.
However, this says nothing about your particular nonconvex optimization problem.

$\begingroup$ Consider a sourcesink flow network that for some nodes in the network, the corresponding outgoing arcs have unknown inputs that require the amount of flow to such a node must be split based on these coefficients. All unknowns are given in some intervals. Now, we need to check if there is a realization of the unknowns in the given intervals such that for the corresponding values, the network is feasible. $\endgroup$ – Star Jul 5 '13 at 6:36

$\begingroup$ I can't make sense of what you've written in the above comment. I'd suggest editing your original question to describe the problem in detail using mathematical notation. $\endgroup$ – Brian Borchers Jul 5 '13 at 14:41