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Convergence of the Newton Method for Aubin Continuous Maps

Ioannis K. Argyros
영남수학회 (Youngnam Mathematical Society)|2009.06|East Asian Mathematical Journal|제25권 제2호|pp. 153-157

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참고문헌

키워드

Banach spaceNewton's methodgeneralized equationAubin continuous map
주제분류수학

초록

Motivated by optimization considerations we revisit the work by Dontchev in [7] involving the convergence of Newton's method to a solution of a generalized equation in a Banach space setting. Using the same hypotheses and under the same computational cost we provide a finer convergence analysis for Newton's method by using more precise estimates.

Abstract

Motivated by optimization considerations we revisit the work by Dontchev in [7] involving the convergence of Newton's method to a solution of a generalized equation in a Banach space setting. Using the same hypotheses and under the same computational cost we provide a finer convergence analysis for Newton's method by using more precise estimates.

참고문헌 (11)

  1. J. P. Aubin, "Lipschitz behavior of solutions to convex minimization problems", Math. Oper. Res, 9, pp.87~111 (1984)
  2. I. K. Argyros, "A unifying local-semilocal convergence analysis and applications for two- point Newton-like methods in Banach space", J. Math. Anal. Appl, 298, pp.374~397 (2004)
  3. I. K. Argyros, "Newton Methods" (2005), Nova Science Publ. Inc
  4. I. K. Argyros, "On the secant method for solving nonsmooth equations", J. Math. Anal. Appl, 322(1), pp.146~157 (2006)
  5. A. L. Dontchev, "An inverse function theorem for set-valued maps", Proc. Amer. Math. Soc, 121, pp.481~484 (1994)
  6. A. L. Dontchev, "Local convergence of the Newton method for generalized equations", C.R. Acad. Sci. Paris, t, 332, pp.327~331 (1996)
  7. A. L. Dontchev, "Uniform convergence of the Newton method for Aubin continuous maps", Serdica Math. J, 22, pp.385~398 (1996)
  8. L. V. Kantorovich, "Pergamon Press" (1982), Pergamon Press
  9. S. M. Robinson, "Newton's method for a class of nonsmooth functions", Set-Valued Anal- ysis, 2, pp.291~305 (1994)
  10. R. T. Rockafellar, "Lipschitz properties of multifunctions", Nonlinear Analysis, 9, pp.867~885 (1985)
  11. B. Xiao, "A nonsmooth Newton method for variational inequalities I", Theory, Math. Programming, 65, pp.151~194 (1994)

관련 논문AI추천

Local convergence of Newton-like methods for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2009 · 제25권 제4호On the convergence of Newton's method for set valued maps under weak conditionsIoannis K. Argyros강원경기수학회 · 한국수학논문집2012 · 제20권 제1호Local Convergence of Newton's Method for Perturbed Generalized EquationsIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2006 · 제13권 제4호Improved convergence results for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2008 · 제24권 제2호ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제1호On the convergence of a Newton-like method under weak conditionsHongmin Ren, Ioannis K. Argyros대한수학회 · 대한수학회논문집2011 · 제26권 제4호

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