  In this paper, a relation between shadow price and the Lagrangian multiplier
for nonsmooth problem is explored. It is shown that the Lagrangian Multiplier
is the upper bound of shadow price for convex optimization and a class of
Lipschtzian optimizations. This work can be used in shadow pricing for
nonsmooth situation. The several nonsmooth functions involved in this class of
Lipschtzian optimizations is listed. Finally, an application to electricity
pricing is discussed.
