A nonlinear complementarity approach for the national energy modeling system

Abstract

0The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the US. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach.We describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, we show that the SCP format is equally valid for a more general form of NEMS. We also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP.

A social-ecological analysis of ecosystem services supply and trade-offs in European wood-pastures

“…To assess the potential geographical influence on the trade-offs, we included the study areas as supplementary variables. Thus, we projected them onto the principal components for interpretative purposes without intervening in the calculation of the eigenvalues ( 58 ). We used the R package PCAmixdata to do the calculations ( 57 ).…”

Engineering and Economic Applications of Complementarity Problems

“…of their work. Specifically, Professors Anders Klarbring and Francis Tin-Loi have helped us with the contact and structural mechanics problems, respectively; Professors Mark Cronshaw and Thomas Rutherford have commented on the general equilibrium section; Dr. Steven Gabriel and Professor Francis Tin-Loi have kindly sent us their preprints of [57,192,194].…”

“…In a proposed complementarity formulation of NEMS [57], the conversion, transmission, and distribution of energy are modeled by four separate nonlinear programs. The mixed nonlinear complementarity problem is formed by augmenting the KKT conditions of these nonlinear programs with various nonlinear equations that link the solution vectors and multipliers to computed fuel prices and quantities.…”

The National Energy Modeling System: A Large-Scale Energy-Economic Equilibrium Model

“…Pang 1992, 1994;Pang and Gabriel 1993, Gabriel and Moré 1997, Gabriel 1998a can simultaneously compute estimates for the NEMS variables (such as fuel prices and quantities). This should be contrasted with the current GaussSeidel/SOR method, which "freezes" the prices and quantities for all but the current module under consideration.…”