본문 바로가기
KERD
논문KCI 등재

New iterative methods for finding a common zero of a finite family of monotone operators in Hilbert spaces

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

The purpose of this paper is to give some new iterative methods for finding a common zero of a finite family of monotone operators in Hilbert spaces. We also give the applications of the obtained result for the convex feasibility problem and constrained convex optimization problem in Hilbert spaces.

Abstract

The purpose of this paper is to give some new iterative methods for finding a common zero of a finite family of monotone operators in Hilbert spaces. We also give the applications of the obtained result for the convex feasibility problem and constrained convex optimization problem in Hilbert spaces.

참고문헌 (26)

  1. V. Barbu, "Convexity and Optimization in Banach spaces" (1978), Editura Academiei R. S. R.
  2. H. H. Bauschke, "Projection and proximal point methods convergence results and counterexamples", Nonlinear Anal, 56(5), pp.715~738 (2004)
  3. H. Brezis, "Produits infinis de resolvantes", Israel J. Math, 29(4), pp.329~345 (1978)
  4. R. E. Bruck, "A strongly convergent iterative solution of 0 2 U(x) for a maximal mono-tone operator U in Hilbert space", J. Math. Anal. Appl, 48, pp.114~126 (1974)
  5. Y. J. Cho, "Viscosity approximation methods for a family of m-accretive mapping in re exive Banach spaces", Positivity, 12(3), pp.483~494 (2008)
  6. K. Goebel, "Topics in Metric Fixed Point Theory" (1990), Cambridge Univ. Press
  7. O. Guler, "On the convergence of the proximal point algorithm for convex minimization", SIAM J. Control Optim, 29(2), pp.403~419 (1991)
  8. B. Halpern, "Fixed points of nonexpanding maps", Bull. Amer. Math. Soc, 73, pp.957~961 (1967)
  9. 정종수, "Strong convergence of an iterative method for finding common zeros of a finite family of accretive operators", 대한수학회논문집, 24(3), pp.381~393 (2009), 대한수학회
  10. S. Kamimura, "Approximating solutions of maximal monotone oper-ators in Hilbert spaces", J. Approx. Theory, 106(2), pp.226~240 (2000)
  11. J. K. Kim, "Viscosity approximation method with Meir-Keeler con-tractions for common zero of accretive operators in Banach spaces", Fixed Point Theory Appl, 2015, pp.17~ (2015)
  12. J. K. Kim, "Approximation common zero of two accretive operators in Banach spaces", Appl. Math. Comput, 283, pp.265~281 (2016)
  13. N. Lehdili, "Combining the proximal algorithm and Tikhonov regular-ization", Optimization, 37(3), pp.239~252 (1996)
  14. G. Marino, "Weak and strong convergence theorems for strict pseudo contractions in Hilbert spaces", J. Math. Anal. Appl, 329(1), pp.336~346 (2007)
  15. O. Nevanlinna, "Strong convergence of contraction semigroups and of iter-ative methods for accretive operators in Banach spaces", Israel J. Math, 32(1), pp.44~58 (1979)
  16. S. Reich, "Weak convergence theorems for nonexpansive mappings in Banach spaces", J. Math. Anal. Appl, 67(2), pp.274~276 (1979)
  17. S. Reich, "Strong convergence theorems for resolvents of accretive operators in Banach spaces", J. Math. Anal. Appl, 75(1), pp.287~292 (1980)
  18. R. T. Rockafellar, "Characterization of the subdifferentials of convex functions", Pacific J. Math, 17, pp.497~510 (1966)
  19. R. T. Rockafellar, "Monotone operators and proximal point algorithm", SIAM J. Control Optim, 14(5), pp.887~897 (1976)
  20. Y. Song, "A note on a paper "A regularization method for the proximal point algorithm"", J. Glob. Optim, 43(1), pp.171~174 (2009)
  21. T. M. Tuyen, "Strong convergence theorem for a common zero of m-accretive mappings in Banach spaces by viscosity approximation methods", Nonlinear Funct. Anal. Appl, 17, pp.187~197 (2012)
  22. H. K. Xu, "Iterative algorithms for nonlinear operators", J. Lond. Math. Soc, 66(1), pp.240~256 (2002)
  23. H. K. Xu, "A regularization method for the proximal point algorithm", J. Global Optim, 36(1), pp.115~125 (2006)
  24. H. K. Xu, "Strong convergence of an iterative method for nonexpansive and accretive op-erators", J. Math. Anal. Appl, 314(2), pp.631~643 (2006)
  25. Y. Yamada, "Inherently parallel algorithms in feasibility and optimization and their applications", pp.473~504 (2001), North-Holland
  26. H. Zegeye, "Strong convergence theorems for a common zero of a finite family of m-accretive mappings", Nonlinear Anal, 66(5), pp.1161~1169 (2007)

관련 논문AI추천

이 간행물의 다른 논문 (25건)