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Local convergence of Newton-like methods for generalized equations

Ioannis K. Argyros
영남수학회 (Youngnam Mathematical Society)|2009.12|East Asian Mathematical Journal|제25권 제4호|pp. 425-431

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참고문헌

키워드

generalized equationsBanach spaceNewton-like methodslocal convergenceradius of convergenceFr\'echet derivativeLipschitz/center-Lipschitz condition.
주제분류수학

초록

We provide a local convergence analysis for Newton-like methods for the solution of generalized equations in a Banach space setting. Using some ideas of ours introduced in [2] for nonlinear equations we show that under weaker hypotheses and computational cost than in [7] a larger convergence radius and finer error bounds on the distances involved can be obtained.

Abstract

We provide a local convergence analysis for Newton-like methods for the solution of generalized equations in a Banach space setting. Using some ideas of ours introduced in [2] for nonlinear equations we show that under weaker hypotheses and computational cost than in [7] a larger convergence radius and finer error bounds on the distances involved can be obtained.

참고문헌 (11)

  1. Aubin, J. -P., "Lipschitz behavior of solutions to convex minimization problems", Math. Oper. Res, 9, pp.87~111 (1984)
  2. Argyros, I. K., "A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space", J. Math. Anal. Applic, 298, pp.374~397 (2004)
  3. Argyros, I. K., "Newton Methods" (2005), Nova Science Publ. Inc
  4. Argyros, I. K., "On the secant method for solving nonsmooth equations", J. Math. Anal. Appl, ~ (2006)
  5. Dontchev, A. L, "An inverse function theorem for set-valued maps", Proc. Amer. Math. Soc, 121, pp.481~484 (1994)
  6. Dontchev, A. L., "Local convergence of the Newton method for generalized equations", C. R. Acad. Sci. Paris, t, 332, pp.327~331 (1996), Mathematical Analysis
  7. Geo ory, M. H, "A local convergence of some iterative methods for generalized equations", J. Math. Anal. Applic, 290, pp.497~505 (2004)
  8. Io e, A. D, "Theory of Extremal Problems", ~ (1979)
  9. Kantorovich, L. V, "Functional Analysis in Normed Spaces" (1982), Pergamon Press
  10. Rockafellar, R. T., "Lipschitz properties of multifunctions", Nonlinear Analysis, 9, pp.867~885 (1985)
  11. Xiao, B, "A nonsmooth Newton method for variational inequalities I: Theory", Math. Programming, 65, pp.151~194 (1994)

관련 논문AI추천

Improved convergence results for generalized equationsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2008 · 제24권 제2호On the convergence of a Newton-like method under weak conditionsHongmin Ren, Ioannis K. Argyros대한수학회 · 대한수학회논문집2011 · 제26권 제4호Convergence of the Newton Method for Aubin Continuous MapsIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2009 · 제25권 제2호On the convergence of Newton's method for set valued maps under weak conditionsIoannis K. Argyros강원경기수학회 · 한국수학논문집2012 · 제20권 제1호ON THE CONVERGENCE OF NEWTON'S METHOD AND LOCALLY HÖLDERIAN INVERSES OF OPERATORSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2009 · 제16권 제1호CONCERNING THE RADII OF CONVERGENCE FOR ACERTAIN CLASS OF NEWTON-LIKE METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제1호

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