Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 1/2021

01.04.2021

Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications

verfasst von: Bing Tan, Xiaolong Qin, Jen-Chih Yao

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.
Vorheriger Artikel An hp-Version Jacobi Spectral Collocation Method for the Third-Kind VIEs
Nächster Artikel Smoothing Strategy Along with Conjugate Gradient Algorithm for Signal Reconstruction

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
2.
Censor, Y., Elfving, T.: A multiprojection algorithms using Bregman projection in a product space. Numer. Algorithms 8, 221–239 (1994)MathSciNetCrossRef
3.
Censor, Y., Bortfeld, T., Martin, B., Trofimov, A.: A unified approach for inversion problems in intensity-modulated radiation therapy. Phys. Med. Biol. 51, 2353–2365 (2006)CrossRef
4.
Censor, Y., Gibali, A., Reich, S.: Algorithms for the split variational inequality problem. Numer. Algorithms 59, 301–323 (2012)MathSciNetCrossRef
5.
Byrne, C.: Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Probl. 18, 441–453 (2002)MathSciNetCrossRef
6.
Combettes, P.L.: The convex feasibility problem in image recovery. Adv. Imaging Electron Phys. 95, 155–270 (1996)CrossRef
7.
Byrne, C., Censor, Y., Gibali, A., Reich, S.: Weak and strong convergence of algorithms for the split common null point problem. J. Nonlinear Convex Anal. 13, 759–775 (2012)MathSciNetMATH
8.
Kazmi, K.R., Rizvi, S.H.: An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping. Optim. Lett. 8, 1113–1124 (2014)MathSciNetCrossRef
9.
Chuang, C.S.: Algorithms with new parameter conditions for split variational inclusion problems in Hilbert spaces with application to split feasibility problem. Optimization 65, 859–876 (2016)MathSciNetCrossRef
10.
Sitthithakerngkiet, K., Deepho, J., Kumam, P.: A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems. Appl. Math. Comput. 250, 986–1001 (2015)MathSciNetMATH
11.
Ceng, L.C., Kobis, E., Zhao, X.: On general implicit hybrid iteration method for triple hierarchical variational inequalities with hierarchical variational inequality constraints. Optimization 69, 1961–1986 (2020)MathSciNetCrossRef
12.
Shehu, Y., Ogbuisi, F.U.: An iterative method for solving split monotone variational inclusion and fixed point problems. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 110, 503–518 (2016)MathSciNetCrossRef
13.
Ceng, L.C., Shang, M.: Generalized Mann viscosity implicit rules for solving systems of variational inequalities with constraints of variational inclusions and fixed point problems. J. Inequal. Appl. 7, 933 (2019)
14.
Alvarez, F., Attouch, H.: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 9, 3–11 (2001)MathSciNetCrossRef
15.
Polyak, B.T.: Some methods of speeding up the convergence of iterative methods. USSR Comput. Math. Math. Phys. 4, 1–17 (1964)MathSciNetCrossRef
16.
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202 (2009)MathSciNetCrossRef
17.
Chuang, C.S.: Hybrid inertial proximal algorithm for the split variational inclusion problem in Hilbert spaces with applications. Optimization 66, 777–792 (2017)MathSciNetCrossRef
18.
Majee, P., Nahak, C.: On inertial proximal algorithm for split variational inclusion problems. Optimization 67, 1701–1716 (2018)MathSciNetCrossRef
19.
20.
21.
Tan, B., Xu, S., Li, S.: Inertial shrinking projection algorithms for solving hierarchical variational inequality problems. J. Nonlinear Convex Anal. 21, 871–884 (2020)MathSciNet
22.
Tan, B., Fan, J., Li, S.: Self-adaptive inertial extragradient algorithms for solving variational inequality problems. Comput. Appl. Math. 40, Article ID 19 (2021)MathSciNetCrossRef
23.
He, B.S.: A class of projection and contraction methods for monotone variational inequalities. Appl. Math. Optim. 35, 69–76 (1997)MathSciNetCrossRef
24.
Thong, D.V., Dung, V.T., Cho, Y.J.: A new strong convergence for solving split variational inclusion problems. Numer. Algorithms 86, 565–591 (2021)
25.
Long, L.V., Thong, D.V., Dung, V.T.: New algorithms for the split variational inclusion problems and application to split feasibility problems. Optimization 68, 2339–2367 (2019)MathSciNetCrossRef
26.
Anh, P.K., Thong, D.V., Dung, V.T.: A strongly convergent Mann-type inertial algorithm for solving split variational inclusion problems. Optim. Eng. 22, 159–185 (2021)MathSciNetCrossRef
27.
López, G., Martín-Márquez, V., Wang, F., Xu, H.K.: Solving the split feasibilty problem without prior knowledge of matrix norms. Inverse Probl. 28, Article ID 085004 (2012)CrossRef
28.
Kesornprom, S., Cholamjiak, P.: Proximal type algorithms involving linesearch and inertial technique for split variational inclusion problem in Hilbert spaces with applications. Optimization 68, 2369–2395 (2019)MathSciNetCrossRef
29.
Gibali, A., Mai, D.T., Vinh, N.T.: A new relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces and its applications. J. Ind. Manag. Optim. 15, Article ID 963 (2019)MathSciNetMATH
30.
Tang, Y.: Convergence analysis of a new iterative algorithm for solving split variational inclusion problems. J. Ind. Manag. Optim. 13, Article ID 1 (2019)
31.
Tang, Y., Gibali, A.: New self-adaptive step size algorithms for solving split variational inclusion problems and its applications. Numer. Algorithms 83, 305–331 (2020)MathSciNetCrossRef
32.
Ceng, L.C., Yuan, Q.: Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems. J. Inequal. Appl. 2019, Article ID 274 (2019)MathSciNetCrossRef
33.
Ceng, L.C., Petruşel, A., Wen, C.F., Yao, J.C.: Inertial-like subgradient extragradient methods for variational inequalities and fixed points of asymptotically nonexpansive and strictly pseudocontractive mappings. Mathematics 7, Article ID 860 (2019)CrossRef
34.
Suantai, S., Kesornprom, S., Cholamjiak, P.: Modified proximal algorithms for finding solutions of the split variational inclusions. Mathematics 7, Article ID 708 (2019)CrossRef
35.
Marino, G., Xu, H.K.: Convergence of generalized proximal point algorithm. Commun. Pure Appl. Anal. 3, 791–808 (2004)MathSciNetCrossRef
36.
Takahashi, W.: Nonlinear Functional Analysis-Fixed Point Theory and Its Applications. Yokohama Publishers, Yokohama (2000)MATH
37.
Chuang, C.S.: Strong convergence theorems for the split variational inclusion problem in Hilbert spaces. Fixed Point Theory Appl. 2013, Article ID 350 (2013)MathSciNetCrossRef
38.
Saejung, S., Yotkaew, P.: Approximation of zeros of inverse strongly monotone operators in Banach spaces. Nonlinear Anal. 75, 742–750 (2012)MathSciNetCrossRef
39.
Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2nd edn. Springer, New York (2017)CrossRef
Metadaten
Titel
Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications
verfasst von
Bing Tan
Xiaolong Qin
Jen-Chih Yao
Publikationsdatum
01.04.2021
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 1/2021
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-021-01428-9

Weitere Artikel der Ausgabe 1/2021

Journal of Scientific Computing 1/2021 Zur Ausgabe

OriginalPaper

Numerical Analysis and Simulation for a Wave Equation with Dynamical Boundary Control

OriginalPaper

Computable Interpolation Error Constants for the Geometric Simplex Finite Elements

OriginalPaper

A High-order Exponential Integrator for Nonlinear Parabolic Equations with Nonsmooth Initial Data

OriginalPaper

Analysis of the Energy Stability for Stabilized Semi-implicit Schemes of the Functionalized Cahn-Hilliard Mass-conserving Gradient Flow Equation

OriginalPaper

A Dimensional Splitting Exponential Time Differencing Scheme for Multidimensional Fractional Allen-Cahn Equations

OriginalPaper

A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions

Premium Partner

    Bildnachweise