Hogan's PIES Example and Lemke's Algorithm.
Abstract
Newton's method for generalized equations (Josephy (3)) was applied to the economic equilibrium problem of the Project Independence Evaluation System (PIES) Energy Model. The resulting algorithm involves solving a sequence of linear complementarity problems. Lemke's complementary pivot algorithm is used for this purpose. In this paper, it is shown that the linear complementarity problems will be copositive plus when the negative of the elasticity matrix, -e, of the consumer's quantity vs. price relation has the following properties: (1) positive diagonals, (2) negative off-diagonals, and (3) strict diagonal dominance. These conditions are satisfied for Hogan's example. Thus, Lemke's algorithm will either converge to a solution or show that no solution exists. Under the conditions of Theorem 1 of Josephy, a solution to the linear complementarity problems will always exist. Hence, Lemke's algorithm can be used when the conditions of the Theorem 1 of Josephy are satisfied.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1979
- Accession Number
- ADA077103
Entities
People
- Norman H. Josephy
Organizations
- University of Wisconsin–Madison