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Newton and other continuation methods for multivalued inclusions

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Abstract

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.

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  1. Place du Maréchal de Lattre de Tassigny, CEREMADE, U.R.A. CNRS 749 Université Paris-Dauphine, 75775, Paris cedex 16, France

    Patrick Saint-Pierre

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Saint-Pierre, P. Newton and other continuation methods for multivalued inclusions. Set-Valued Anal 3, 143–156 (1995). https://doi.org/10.1007/BF01038596

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