Volume 21, No 2, 2014, P. 84–101

UDC 519.865.3
V. I. Shmyrev
Polyhedral complementarity algorithms for searching an equilibrium in linear models of competitive economy

Abstract:
The article represents a review of the author’s papers about an original approach to the equilibrium problem in linear exchange models. The conceptual base of this approach is the scheme of polyhedral complementarity. The approach may be considered as a realization of the main idea of the simplex-method of linear programming. It has no analogs and made it possible to obtain the finite algorithms for some variations of the classical exchange model. In addition it allows us to reveal a monotonicity property inherent in the models under consideration. The similar one can be seen in linear complementarity problems with positive principal minors of the restriction matrix (class [P]).
Ill. 9, bibliogr. 24.

Keywords: exchange model, economic equilibrium, price vector, polyhedral complementarity, fixed point, mapping’s monotonicity, finite algorithm.

Shmyrev Vadim Ivanovich ^1,2
1. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: shvi@math.nsc.ru