The National Energy Modeling System (NEMS) is a large-scale mathematical mo
del that computes equilibrium fuel prices and quantities in the U.S. energy
sector and is currently in use at the U.S. Department of Energy (DOE). At
present, to generate these equilibrium values, NEMS iteratively solves a se
quence of linear programs and nonlinear equations. This is a nonlinear Gaus
s-Seidel approach to arrive at estimates of market equilibrium fuel prices
and quantities. In this paper, we present existence and uniqueness results
for NEMS-type models based on a nonlinear complementarity/variational inequ
ality problem format. Also, we document mathematically, for the first time,
how the inputs and the outputs for each NEMS module link together.