Set-Valued Analysis

, Volume 3, Issue 2, pp 143–156 | Cite as

Newton and other continuation methods for multivalued inclusions

  • Patrick Saint-Pierre


Viability theory provides an efficient framework for looking for zeros of multivalued equations: 0 ∈F(x). The main idea is to consider solutions of a suitable differential inclusion, viable in graph ofF. The choice of the differential inclusion is guided necessarily by the fact that any solution should converge or go through a zero of the multivalued equation. We investigate here a new understanding of the well-known Newton's method, generalizing it to set-valued equations and set up a class of algorithms which involve generalization of some homotopic path algorithms.

Mathematics Subject Classification (1991)

26E25 34A60 49Mxx 

Key words

multivalued equations Newton's method equilibria homotopic methods 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Patrick Saint-Pierre
    • 1
  1. 1.Place du Maréchal de Lattre de TassignyCEREMADE, U.R.A. CNRS 749 Université Paris-DauphineParis cedex 16France

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