An odd theorem-Reference-Cited by-同舟云学术

An odd theorem

Published:1970 Issue:3 Volume:26 Page:509-513
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Eaves B. Curtis

Abstract

Let C C be a bounded convex polyhedral set and let f : C → C f:C \to C be continuous and piecewise linear. Using notions from complementary pivot theory, it is shown that if each fixed point of f f lies interior to some piece of linearity, then f f has an odd number of fixed points. In addition, an algorithm is given for computing a fixed point of f f .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1970-026-03/S0002-9939-1970-0270757-2/S0002-9939-1970-0270757-2.pdf

Reference12 articles.

1. Complementary pivot theory of mathematical programming;Cottle, Richard W.;Linear Algebra Appl.,1968

2. B. Curtis Eaves, Linear complementarity problem in mathematical programming, Doctoral Dissertation, Stanford University, Stanford, Calif., 1969.

3. Bimatrix equilibrium points and mathematical programming;Lemke, C. E.;Management Sci.,1964

4. Equilibrium points of bimatrix games;Lemke, C. E.;J. Soc. Indust. Appl. Math.,1964

5. K. G. Murty, On the number of solutions to the complementary quadratic programming problem, Doctoral Dissertation, Engineering Science, University of California, Berkeley, Calif., 1968.

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