Hogan's PIES example and Lemke's algorithm. Technical summary report
Newton's method for generalized equations 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.
- Research Organization:
- Wisconsin Univ., Madison (USA). Mathematics Research Center
- OSTI ID:
- 5147929
- Report Number(s):
- AD-A-077103
- Country of Publication:
- United States
- Language:
- English
Similar Records
On solving linear complementarity problems with sufficient matrices by Lemke`s method
The equivalence of Dantzig's self-dual parametric algorithm for linear programs to Lemke's algorithm for linear complementarity problems applied to linear programs: Technical report