Homotopy method
From HandWiki
Short description: Method for fixed-point computation
 | This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
(Learn how and when to remove this template message)
|
The homotopy method is a method for fixed-point computation, based on the mathematical concept of homotopy. The method was devised in 1972 by B. Curtis Eaves.[1]
Given a function f, for which we want to find a fixed point, the algorithm works by starting with an affine function that approximates f, and deforming it towards f while following the fixed point.
Applications
The homotopy method has been used for market equilibrium computation.[2]
Further reading
The method is further explained in a book by Michael Todd,[3] which surveys various algorithms developed until 1976.
References
- ↑ Eaves, B. Curtis (December 1972). "Homotopies for computation of fixed points". Mathematical Programming 3-3 (1): 1–22. doi:10.1007/BF01584975.
- ↑ Codenotti, Bruno; Pemmaraju, Sriram; Varadarajan, Kasturi (2004-12-01). "The computation of market equilibria". SIGACT News 35 (4): 23–37. doi:10.1145/1054916.1054927. ISSN 0163-5700. https://doi.org/10.1145/1054916.1054927.
- ↑ The Computation of Fixed Points and Applications. Lecture Notes in Economics and Mathematical Systems. 124. 1976. doi:10.1007/978-3-642-50327-6. ISBN 978-3-540-07685-8.
 |  |
