Newton and other continuation methods for multivalued inclusions
Saint-Pierre, Patrick (1995), Newton and other continuation methods for multivalued inclusions, Set-Valued Analysis, 3, 2, p. 143-156. http://dx.doi.org/10.1007/BF01038596
TypeArticle accepté pour publication ou publié
Journal nameSet-Valued Analysis
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Abstract (EN)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.
Subjects / Keywordsmultivalued equations; Newton's method; equilibria; homotopic methods
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