On Newton's method for solving generalized equations |
| |
| Institution: | 1. Instituto de Matemática e Estatística, Universidade Federal de Goiás, CP-131, CEP 74001-970, Goiânia, GO, Brazil;2. Département de Mathématiques et Informatique, Laboratoire LAMIA, EA4540, Université des Antilles, Campus de Fouillole, 97159, Pointe-à-Pitre, France;3. Universidade Federal do Piauí, Departamento de Matemática, CEP 64049-550, Teresina, PI, Brazil;1. Universidad Nacional de Hurlingham, Instituto de Tecnología e Ingeniería, Av. Gdor. Vergara 2222 (B1688GEZ), Villa Tesei, Buenos Aires, Argentina;2. Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150 (B1613GSX), Los Polvorines, Buenos Aires, Argentina;3. National Council of Science and Technology (CONICET), Argentina;4. Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150 (B1613GSX), Los Polvorines, Buenos Aires, Argentina;1. Department of Mathematics, University of Innsbruck, Austria;2. IRIF, Université de Paris, France;3. Institute for Theoretical Physics, University of Innsbruck, Austria |
| |
| Abstract: | In this paper, we study the convergence properties of a Newton-type method for solving generalized equations under a majorant condition. To this end, we use a contraction mapping principle. More precisely, we present semi-local convergence analysis of the method for generalized equations involving a set-valued map, the inverse of which satisfying the Aubin property. Our analysis enables us to obtain convergence results under Lipschitz, Smale and Nesterov-Nemirovski's self-concordant conditions. |
| |
| Keywords: | Generalized equations Newton's method Aubin property Majorant condition |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
