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
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben
Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 2/2023

10.12.2022 | Original Research

A hybrid BB-type method for solving large scale unconstrained optimization

verfasst von: Jian Gao, Yigui Ou

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 2/2023

Einloggen

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

search-config
loading …

Abstract

In this paper, based on the ideas of Barzilai and Borwein (BB) method and IMPBOT algorithm proposed by Brown and Biggs (J Optim Theory Appl 62:211–224, 1989), we propose a hybrid BB-type method with a nonmonotone line search for solving large scale unconstrained optimization problems. Under mild conditions, the global convergence of the proposed method is analyzed. Numerical testing results and related comparisons are also reported to show the efficiency and robustness of the proposed hybrid method, especially for highly nonlinear optimization problems.
Vorheriger Artikel Dynamics of a stochastic predator-prey model with fear effect and hunting cooperation
Nächster Artikel q-Fibonacci sequence spaces and related matrix transformations

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
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
2.
Jiang, X.Z., Liao, W., Yin, J.H., Jian, J.B.: A new family of hybrid three-term conjugate gradient methods with applications in image restoration. Numer. Algorithms 91, 161–191 (2022)MathSciNetMATHCrossRef
3.
Liu, Y.F., Zhu, Z.B., Zhang, B.X.: Two sufficient descent three-term conjugate gradient methods for unconstrained optimization problems with applications in compressive sensing. J. Appl. Math. Comput. 68, 1787–1816 (2022)MathSciNetMATHCrossRef
4.
5.
Raydan, M.: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7, 26–33 (1997)MathSciNetMATHCrossRef
6.
Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton’s method. SIAM J. Numer. Anal. 23, 707–716 (1986)MathSciNetMATHCrossRef
7.
Xiao, Y.H., Wang, Q.Y., Wang, D.: Notes on the Dai-Yuan-Yuan modified spectral gradient method. J. Comput. Appl. Math. 234, 2986–2992 (2010)MathSciNetMATHCrossRef
8.
Cruz, W., Noguera, G.: Hybrid spectral gradient method for the unconstrained minimization problem. J. Glob. Optim. 44, 193–212 (2009)MathSciNetMATHCrossRef
9.
10.
Arzani, F., Reza Peyghami, M.: A new nonmonotone filter Barzilai–Borwein method for solving unconstrained optimization problems. Int. J. Comput. Math. 93, 596–608 (2016)MathSciNetMATHCrossRef
11.
Lakhbab, H., Bernoussi, S.E.: Hybrid nonmonotone spectral gradient method for the unconstrained minimization problem. Comput. Appl. Math. 36, 1421–1430 (2017)MathSciNetMATHCrossRef
12.
Dai, Y.H., Huang, Y.K., Liu, X.W.: A family of spectral gradient methods for optimization. Comput. Optim. Appl. 74, 43–65 (2019)MathSciNetMATHCrossRef
13.
Sim, H.S., Chen, C.Y., Leong, W.J., Li, J.: Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization. J. Ind. Manag. Optim. (2021), Published online, https://​doi.​org/​10.​3934/​jimo.​2021143
14.
Serafino, D., Ruggiero, V., Toraldo, G., Zanni, L.: On the steplength selection in gradient methods for unconstrained optimization. Appl. Math. Comput. 318, 176–195 (2018)MathSciNetMATH
15.
Liu, Z.X., Liu, H.W.: An efficient gradient method with approximate optimal stepsize for large-scale unconstrained optimization. Numer. Algorithms 78, 21–39 (2018)MathSciNetMATHCrossRef
16.
Liu, Z.X., Chu, W.L., Liu, H.W., Liu, Z.: An efficient gradient method with approximately optimal stepsizes based on regularization models for unconstrained optimization. RAIRO Oper. Res. 56, 2403–2424 (2022)MathSciNetMATHCrossRef
17.
18.
Sun, C., Zhang, Y.: A brief review on gradient method. Oper. Res. Trans. 25, 119–132 (2021)MathSciNet
19.
Brown, A.A., Biggs, M.C.: Some effective methods for unconstrained optimization based on the solution of system of ordinary differentiable equations. J. Optim. Theory Appl. 62, 211–224 (1989)MathSciNetMATHCrossRef
20.
21.
Han, L.X.: On the convergence properties of an ODE algorithm for unconstrained optimization. Math. Numer. Sin. 15, 449–455 (1993)MathSciNetMATH
22.
23.
Zhang, L.H., Kelley, C.T., Liao, L.Z.: A continuous Newton-type method for unconstrained optimization. Pac. J. Optim. 4, 257–277 (2008)MathSciNetMATH
24.
Luo, X.L., Kelley, C.T., Liao, L.Z., Tam, H.W.: Combining trust-region techniques and Rosenbrock methods to compute stationary points. J. Optim. Theory Appl. 140, 265–286 (2009)MathSciNetMATHCrossRef
25.
Ou, Y.G., Liu, Y.Y.: An ODE-based nonmonotone method for unconstrained optimization problems. J. Appl. Math. Comput. 42, 351–369 (2013)MathSciNetMATHCrossRef
26.
27.
Chen, J., Qi, L.Q.: Pseudotransient continuation for solving systems of nonsmooth equations with inequality constraints. J. Optim. Theory Appl. 147, 223–242 (2010)MathSciNetMATHCrossRef
28.
Wang, L., Li, Y., Zhang, L.W.: A differential equation method for solving box constrained variational inequality problems. J. Ind. Manag. Optim. 7, 183–198 (2011)MathSciNetMATHCrossRef
29.
Kelley, C.T., Liao, L.Z.: Explicit pseudo-transient continuation. Pac. J. Optim. 9, 77–91 (2013)MathSciNetMATH
30.
31.
Tan, Z.Z., Hu, R., Fang, Y.P.: A new method for solving split equality problems via projection dynamical systems. Numer. Algorithms 86, 1705–1719 (2021)MathSciNetMATHCrossRef
32.
Luo, X.L., Xiao, H., Lv, J.H., Zhang, S.: Explicit pseudo-transient continuation and the trust-region updating strategy for unconstrained optimization. Appl. Numer. Math. 165, 290–302 (2021)MathSciNetMATHCrossRef
33.
Sun, W.Y., Yuan, Y.X.: Optimization Theory and Methods: Nonlinear Programming. Springer Optimization and its Applications, vol. 1. Springer, New York, (2006)
34.
Wei, Z.X., Li, G.Y., Qi, L.Q.: New quasi-Newton methods for unconstrained optimization problems. Appl. Math. Comput. 175, 1156–1188 (2006)MathSciNetMATH
35.
Zhang, J.Z., Deng, N.Y., Chen, L.H.: New quasi-Newton equation and related methods for unconstrained optimization. J. Optim. Theory Appl. 102, 147–167 (1999)MathSciNetMATHCrossRef
36.
Li, D.H., Fukushima, M.: A modified BFGS method and its global convergence in nonconvex minimization. J. Comput. Appl. Math. 129, 15–35 (2001)MathSciNetMATHCrossRef
37.
38.
Gu, N.Z., Mo, J.T.: Incorporating nonmonotone strategies into the trust region method for unconstrained optimization. Comput. Math. Appl. 55, 2158–2172 (2008)MathSciNetMATHCrossRef
39.
Zhang, H.C., Hager, W.W.: A nonmonotone line search technique and its applications to unconstrained optimization. SIAM J. Optim. 14, 1043–1056 (2004)MathSciNetMATHCrossRef
40.
Hager, W.W., Zhang, H.C.: A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16, 170–192 (2005)MathSciNetMATHCrossRef
41.
Andrei, N.: An unconstrained optimization test functions collection. Adv. Model. Optim. 10, 147–161 (2008)MathSciNetMATH
42.
Gould, N.I.M., Orban, D., Toint, P.L.: CUTEr: A constrained and unconstrained testing environment, revised. Trans. Math. Softw. 29, 373–394 (2003)MATHCrossRef
43.
Dolan, E.D., More, J.J.: Benchmarking optimization software with performance profiles. Math. Program. Ser. A 91, 201–213 (2002)MathSciNetMATHCrossRef
Metadaten
Titel
A hybrid BB-type method for solving large scale unconstrained optimization
verfasst von
Jian Gao
Yigui Ou
Publikationsdatum
10.12.2022
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 2/2023
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-022-01826-8

Weitere Artikel der Ausgabe 2/2023

Journal of Applied Mathematics and Computing 2/2023 Zur Ausgabe

Original Research

Dynamical analysis of a stochastic non-autonomous SVIR model with multiple stages of vaccination

Original Research

Some quantum synchronizable codes with explicit distance

Original Research

Partial permanence and stationary distribution of a stochastic competitive model with feedback controls and distributed delays

Original Research

Mathematical models and dynamic behaviors of cancer treatment by continuous and pulsed radiotherapy

Original Research

Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts

Original Research

Numerical algorithms for corner-modified symmetric Toeplitz linear system with applications to image encryption and decryption

Premium Partner

    Bildnachweise