Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 66, 2017 - Issue 7
178
Views
15
CrossRef citations to date
0
Altmetric
Original Articles

Generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces

, &
Pages 1105-1117 | Received 03 Oct 2016, Accepted 26 Apr 2017, Published online: 16 May 2017

References

  • Byrne C. A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Prob. 2004;20:103–120.
  • Combettes PL, Wajs VR. Signal recovery by proximal forward-backward splitting. Multiscale Model Simul. 2005;4:1168–1200.
  • Sra S, Nowozin S, Wright SJ. Optimization for machine learning. Neural information processing series. Cambridge (MA): MIT Press; 2011.
  • Lions PL, Mercier B. Splitting algorithms for the sum of two nonlinear operators. SIAM J Numer Anal. 1979;16:964–979.
  • Tseng P. A modified forward--backward splitting method for maximal monotone mappings. SIAM J Control Optim. 2000;38:431–446.
  • Chen GHG, Rockafellar RT. Convergence rates in forward--backward splitting. SIAM J Optim. 1997;7:421–444.
  • Güler O. On the convergence of the proximal point algorithm for convex minimization. SIAM J Control Optim. 1991;29:403–419.
  • Rockafellar RT. Monotone operators and the proximal point algorithm. SIAM J Control Optim. 1976;14:877–898.
  • Takahashi W, Wong NC, Yao JC. Two generalized strong convergence theorems of Halpern’s type in Hilbert spaces and applications. Taiwanese J. Math. 2012;16:1151–1172.
  • López G, Martín-Márquez V, Wang F, et al. Forward--backward splitting methods for accretive operators in Banach spaces. Abstr Appl Anal. 2012;2012:25 p.
  • Moudafi A. Viscosity approximation methods for fixed-points problems. J Math Anal Appl. 2000;241:46–55.
  • Xu HK, Alghamdi MA, Shahzad N. The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces. Fixed Point Theory Appl. 2015;2015:41.
  • Cholamjiak P. A generalized forward--backward splitting method for solving quasi inclusion problems in Banach spaces. Numer Algor. 2016;71:915–932. DOI:10.1007/s11075-015-0030-6
  • Cioranescu I. Geometry of Banach spaces, duality mappings and nonlinear problems. Dordrecht: Kluwer Academic; 1990.
  • Zhou HY. Iterative methods of fixed points and zeros with applications. Beijing: National Defense Industry Press; 2016.
  • Reich S. Strong convergence theorems for resolvents of accretive operators in Banach spaces. J Math Anal Appl. 1980;75:287–292.
  • Maingǐe PE. Approximation method for common fixed points of nonexpansive mappings in Hilbert spaces. J Math Anal Appl. 2007;325:469–479.
  • He S, Yang C. Solving the variational inequality problem defined on intersection of finite level sets. Abstr Appl Anal. 2013;2013:8 p.
  • Rockafellar RT. On the maximality of sums of nonlinear monotone operators. Trans Am Math Soc. 1970;149:75–88.
  • Combettes PL. Iterative construction of the resolvent of a sum of maximal monotone operators. J Convex Anal. 2009;16:727–748.
  • Kamimura S, Takahashi W. Approximating solutions of maximal monotone operators in Hilbert spaces. J Approx Theory. 2000;106:226–240.
  • Marino G, Xu HK. Convergence of generalized proximal point algorithm. Comm Pure Appl. Anal. 2004;3:791–808.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.