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
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Numerical Algorithms
Erschienen in: Numerical Algorithms 1/2021

22.07.2020 | Original Paper

Convergence of discrete approximation for differential linear stochastic complementarity systems

verfasst von: Jianfeng Luo, Xiaozhou Wang, Yi Zhao

Erschienen in: Numerical Algorithms | Ausgabe 1/2021

Einloggen

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

search-config
loading …

Abstract

In this paper, we investigate a class of differential linear stochastic complementarity system consisting of an ordinary differential equation and a stochastic complementarity problem. The existence of solutions for such system is obtained under two cases of the coefficient matrix of the linear stochastic complementarity problem: P-matrix and positive semi-definite matrix. As for the first case, the sample average approximate method and time-stepping method are adopted to get the numerical solutions. Furthermore, a regularization approximation is introduced to the second case to ensure the uniqueness of solutions. The corresponding convergence analysis is conducted, and numerical examples are presented to illustrate the convergence results we derived. Finally, we provide numerical results which come from applications involving dynamic traffic flow problems to support our theorems.
Vorheriger Artikel The Bakhvalov mesh: a complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems
Nächster Artikel On the linear convergence of circumcentered isometry methods

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

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

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
Literatur
1.
Aubin, J.P., Cellina, A.: Differential Inclusions: Set-Valued Maps and Viability Theory. Springer, Berlin (1984)CrossRef
2.
Ban, X., Pang, J.S., Liu, H.X., Ma, R.: Continuous-time point-queue models in dynamic network loading. Transport. Res. B-Meth. 46, 360–380 (2012)CrossRef
3.
Ban, X., Pang, J.S., Liu, H.X., Ma, R.: Modeling and solving continuous-time instantaneous dynamic user equilibria: a differential complementarity systems approach. Transport. Res. B- Meth. 46, 389–408 (2012)CrossRef
4.
Ban, X., Liu, H.X., Ferris, M.C., Ran, B.: A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations. Transport. Res. B- Meth. 42(9), 823–842 (2008)CrossRef
5.
Camlibel, M.K., Pang, J.S., Shen, J.L.: Lyapunov stability of complementarity and extended systems. SIAM J. Optim. 17, 1056–1101 (2006)MathSciNetCrossRef
6.
Chen, X.J., Sun, H.L., Xu, H.F.: Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems. Math. Program. Ser. A 177, 255–289 (2019)MathSciNetCrossRef
7.
Chen, X.J., Wang, Z.Y.: Convergence of regularized time-stepping methods for differential variational inequalities. SIAM J. Optim. 23, 1647–1671 (2013)MathSciNetCrossRef
8.
Chen, X.J., Wang, Z.Y.: Differential variational inequality approach to dynamic games with shared constraints. Math. Program., Ser. A 146, 379–408 (2014)MathSciNetCrossRef
9.
Chen, X.J., Xiang, S.H.: Perturbation bounds of P-matrix linear complementary problems. SIAM J. Optim. 18, 1250–1265 (2007)MathSciNetCrossRef
10.
Chen, X.J., Xiang, S.H.: Newton iterations in implicit time-stepping scheme for differential linear complementarity systems. Math. Program. Ser. A 138, 579–606 (2013)MathSciNetCrossRef
11.
Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003)MATH
12.
Han, L.S., Tiwari, A., Camlibel, M.K., Pang, J.S.: Convergence of time-steeping schemes for passive and extended linear complementarity system. SIAM J. Numer. Anal. 47, 3768–3796 (2009)MathSciNetCrossRef
13.
Jiang, J., Shi, Y., Wang, X.Z., Chen, X.J.: Regularized two-stage stochastic variational inequalities for Cournot-Nash equilibrium under uncertainty. J. Comput. Math. 37, 813–842 (2019)MathSciNetCrossRef
14.
15.
Lang, S.: Real and Fuctional Analysis, 3rd edn. Springer, Berlin (1993)CrossRef
16.
Pang, J.S., Stewart, D.E.: Differential variational inequalities. Math. Program. Ser. A 113, 345–424 (2008)MathSciNetCrossRef
17.
Pang, J.S., Stewart, D.E.: Solution dependence on initial conditions in differential variational inequalities. Math. Program. Ser. B 116, 429–460 (2009)MathSciNetCrossRef
18.
Pang, J.S., Han, L., Ramadurai, G., Ukkusuri, S.: A continuous-time linear complementarity system for dynamic user equilibria in single bottleneck traffic flows. Math. Program. Ser. A 133, 437–460 (2012)MathSciNetCrossRef
19.
Ran, B., Boyce, D.E.: Modelling Dynamic Transportation Networks: an Intelligent Transportation System Oriented Approach. Springer, Berlin (1996)CrossRef
20.
Richard, C.W., Pang, J.S., Richard, S.E.: The linear complementarity problem academic press (1992)
21.
Rockafellar, R.T., Sun, J.: Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging. Math. Program. Ser. B 174, 1–19 (2018)
22.
Rockafellar, R.T., Wets, R. J.-B.: Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16, 119–147 (1991)MathSciNetCrossRef
23.
Ruszczynski, A., Shapiro, A.: Handbook in Operations Research and Management Science, 10: Stochastic Programming. North-Holland, Amsterdam (2003)
24.
Shapiro, A., Dentcheva, D., Ruszczyński, A.: Lectures on stochastic programming: modeling and theory. SIAM (2009)
25.
Stewart, D.E.: Uniqueness for index-one differential variational inequalities. Nonlinear Anal. Hybri. 2, 812–818 (2008)MathSciNetCrossRef
26.
Stewart, D.E.: Uniqueness for solutions of differential complementarity problems. Math. Program. Ser. A 118, 327–345 (2009)MathSciNetCrossRef
27.
Stromberg, K.R.: Introduction to Classical Real Analysis. Wadsworth, Inc., Belmont (1981)MATH
28.
Sun, H.L., Chen, X.J.: Two-stage stochastic variational inequalities theory, algorithms and applications. J. Oper. Res. Soc. China 1–32 (2019)
29.
Wu, S.L., Chen, X.J.: A parallel iterative algorithm for differential linear complementarity problems. SIAM J. Numer. Anal. 55, A3040–A3066 (2017)MathSciNetMATH
30.
Wu, S.L., Zhou, T., Chen, X.J. A Gauss-Seidel type method for dynamic nonlinear complementarity problems, submitted
Metadaten
Titel
Convergence of discrete approximation for differential linear stochastic complementarity systems
verfasst von
Jianfeng Luo
Xiaozhou Wang
Yi Zhao
Publikationsdatum
22.07.2020
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 1/2021
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00965-y

Weitere Artikel der Ausgabe 1/2021

Numerical Algorithms 1/2021 Zur Ausgabe

Original Paper

Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers

Original Paper

Solving interval linear least squares problems by PPS-methods

Original Paper

Generalizing the trapezoidal rule in the complex plane

Original Paper

P1 finite element methods for a weighted elliptic state-constrained optimal control problem

Original Paper

On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes

Original Paper

A central-line coarse preconditioner for Stokes flows in artery-like domains