This talk will address the problem of developing a distributed scheme
for allocating bandwidth to optimize the total system utility for
users having non-convex (sigmoidal) utility functions. Such non-convex
functions are natural in the context of many applications but most of
the work in literature only deals with the simple convex case. The
non-convexity results in the insufficiency of the Karush-Kuhn-Tucker
conditions to identify optimality conditions as well as
non-differentiability of the dual.  We show that a pricing based
mechanism in the dual formulation can be developed based on the theory
of sub-differentials with the properties that the prices
"self-regulate" the users to access the resource or not based on the
net utility. We discuss the convergence issues and show that such an
algorithm can be efficient in the sense of achieving the social
optimal when there are many users.