Newton and other continuation methods for multivalued inclusions |
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Authors: | Patrick Saint-Pierre |
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Affiliation: | (1) Place du Maréchal de Lattre de Tassigny, CEREMADE, U.R.A. CNRS 749 Université Paris-Dauphine, 75775 Paris cedex 16, France |
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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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Keywords: | 26E25 34A60 49Mxx |
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