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
Cognitive Computation
Erschienen in: Cognitive Computation 3/2014

01.09.2014

A Gradient-Based Neural Network Method for Solving Strictly Convex Quadratic Programming Problems

verfasst von: Alireza Nazemi, Masoomeh Nazemi

Erschienen in: Cognitive Computation | Ausgabe 3/2014

Einloggen

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

search-config
loading …

Abstract

In this paper, we study a gradient-based neural network method for solving strictly convex quadratic programming (SCQP) problems. By converting the SCQP problem into a system of ordinary differential equation (ODE), we are able to show that the solution trajectory of this ODE tends to the set of stationary points of the original optimization problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. It is also found that a larger scaling factor leads to a better convergence rate of the trajectory. The simulation results also show that the proposed neural network is feasible and efficient. The simulation results are very attractive.
Vorheriger Artikel A Voting Optimized Strategy Based on ELM for Improving Classification of Motor Imagery BCI Data
Nächster Artikel Conjugate Unscented FastSLAM for Autonomous Mobile Robots in Large-Scale Environments

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 "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"

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
Literatur
1.
Agrawal SK, Fabien BC. Optimization of dynamic systems. Netherlands: Kluwer Academic Publishers; 1999.CrossRef
2.
Ai W, Song YJ, Chen YP. An improved neural network for solving optimization of quadratic programming problems. In: Proceedings of the fifth international conference on machine learning and cybernetics, Dalian; 2006. p.13–6.
3.
Anguita D, Boni A. Improved neural network for SVM learning. IEEE Trans Neural Netw. 2002;13:1243–44.PubMedCrossRef
4.
Avriel M. Nonlinear programming: analysis and methods. Englewood Cliffs, NJ: Prentice-Hall; 1976.
5.
Bazaraa MS, Sherali HD, Shetty CM. Nonlinear programming—theory and algorithms, 2nd ed. New York: Wiley; 1993.
6.
Bertsekas DP. Parallel and distributed computation: numerical methods. Englewood Cliffs, NJ: Prentice-Hall; 1989.
7.
Boggs PT, Domich PD, Rogers JE. An interior point method for general large-scale quadratic programming problems. Ann Oper Res. 1996;62:419–37.CrossRef
8.
Boland NL. A dual-active-set algorithm for positive semi-definite quadratic programming. Math Program. 1996;78:1–27.CrossRef
9.
Boyd S, Vandenberghe L. Convex optimization. Cambridge: Cambridge University Press; 2004.CrossRef
10.
Facchinei F, Jiang H, Qi L. A smoothing method for mathematical programs with equilibrium constraints. Math Program. 1999;35:107-34.CrossRef
11.
Fletcher R. Practical methods of optimization. New York: Wiley; 1981.
12.
Hale JK. Ordinary differential equations. New York: Wiley-Interscience; 1969.
13.
Hu SL, Huang ZH, Chen JS. Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems. J Comput Appl Math. 2009;230:69–82.CrossRef
14.
Huang YC. A novel method to handle inequality constraints for convex programming neural network. Neural Process Lett. 2002;16:17–27.CrossRef
15.
Jiang M, Zhao Y, Shen Y. A modified neural network for linear variational inequalities and quadratic optimization problems. Lecture Notes in Computer Science, 5553, Springer, Berlin: Heidelberg; 2009.p. 1–9.
16.
Kalouptisidis N. Signal processing systems, theory and design. New York: Wiley; 1997.
17.
Kennedy MP, Chua LO. Neural networks for nonlinear programming. IEEE Trans Circuits Syst. 1988;35:554–62.CrossRef
18.
Lillo WE, Loh MH, Hui S, Zăk SH. On solving constrained optimization problems with neural networks: a penalty method approach. IEEE Trans Neural Netw. 1993;4(6):931–39.PubMedCrossRef
19.
Liu Q, Cao J. Global exponential stability of discrete-time recurrent neural network for solving quadratic programming problems subject to linear constraints. Neurocomputing. 2011;74:3494–01.CrossRef
20.
Liu Q, Wang J. A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming. IEEE Trans Neural Netw. 2008;19:558–70.PubMedCrossRef
21.
Liu Q, Zhao Y. A continuous-time recurrent neural network for real-time support vector regression. In: Computational Intelligence in Control and Automation (CICA), 2013 IEEE Symposium on, 16–19 April 2013; p. 189–193.
22.
Maa CY, Shanblatt MA. Linear and quadratic programming neural network analysis. IEEE Trans Neural Netw. 1992;3(4):580–94.PubMedCrossRef
23.
Malek A, Yashtini M. Image fusion algorithms for color and gray level images based on LCLS method and novel artificial neural network. Neurocomputing. 2010;73:937–43.CrossRef
24.
Miller RK, Michel AN. Ordinary differential equations. NewYork: Academic Press; 1982.
25.
More JJ, Toroaldo G. On the solution of large quadratic programming problems with bound constraints. SIAM J Optim. 1991;1:93–13.CrossRef
26.
Nazemi AR. A dynamical model for solving degenerate quadratic minimax problems with constraints. J Comput Appl Math. 2011;236:1282–95.CrossRef
27.
Nazemi AR. A dynamic system model for solving convex nonlinear optimization problems. Commun Nonlinear Sci Numer Simul. 2012;17:1696–05.CrossRef
28.
Nazemi AR, Omidi F. A capable neural network model for solving the maximum flow problem. J Comput Appl Math. 2012;236:3498–13.CrossRef
29.
Nazemi AR, Omidi F. An efficient dynamic model for solving the shortest path problem. Transp Res Part C Emerg Technol. 2013;26:1–19.CrossRef
30.
Pan S-H, Chen J-S. A semismooth Newton method for the SOCCP based on a one-parametric class of SOC complementarity functions. Comput Optim Appl. 2010;45:59–88.CrossRef
31.
Pyne IB. Linear programming on a electronic analogue computer. Trans Am Inst Elect Eng. 1956;75:139-43.
32.
Quarteroni A, Sacco R, Saleri F. Numerical mathematics. Texts in applied mathematics, vol. 37, 2nd ed. Berlin: Springer; 2007.
33.
Sun D, Sun J. Strong semismoothness of the Fischer–Burmeister SDC and SOC complementarity functions. Math Program. 2005;103(3):575–81.CrossRef
34.
Sun J, Zhang L. A globally convergent method based on Fischer–Burmeister operators for solving second-order cone constrained variational inequality problems. Comput Math Appl. 2009;58:1936–46.CrossRef
35.
Sun J, Chen J-S, Ko C-H. Neural networks for solving second-order cone constrained variational inequality problem. Comput Optim Appl. 2012;51:623–48.CrossRef
36.
Tao Q, Cao J, Sun D. A simple and high performance neural network for quadratic programming problems. Appl Math Comput. 2001;124:251–60.CrossRef
37.
Xia Y, Feng G. An improved network for convex quadratic optimization with application to real-time beamforming. Neurocomputing. 2005;64:359–74.CrossRef
38.
Xia Y, Wang J. Primal neural networks for solving convex quadratic programs. In: International joint conference on neural networks; 1999. p. 582–87.
39.
Xia Y, Wang J. A recurrent neural network for solving linear projection equations. Neural Netw. 2000;13:337–50.PubMedCrossRef
40.
Xia Y, Wang J. A general projection neural network for solving monotone variational inequality and related optimization problems. IEEE Trans Neural Netw. 2004;15:318–28.PubMedCrossRef
41.
Xia Y, Wang J. A one–layer recurrent neural network for support vector machine learning. IEEE Trans Syst Man Cybern Part B: Cybern. 2004;34:1261–69.CrossRef
42.
Xia Y, Leung H, Wang J. A projection neural network and its application to constrained optimization problems. IEEE Trans Circuits Syst. 2002;49:447–58.CrossRef
43.
Xia Y, Feng G. Solving convex quadratic programming problems by an modefied neural network with exponential convergence. IEEE International Conference Neural Networks and Signal Processing, Nanjing, China; 2003. p. 14–17.
44.
Xia Y, Feng G, Wang J. A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equation. Neural Networks. 2004;17:1003–15.PubMedCrossRef
45.
Xue X, Bian W. A project neural network for solving degenerate convex quadratic program. Neurocomputing. 2007;70:2449–59.CrossRef
46.
Yang Y, Cao J. A feedback neural network for solving convex constraint optimization problems. Appl Math Comput. 2008;201:340–50.CrossRef
47.
Zhang J, Zhang L. An augmented lagrangian method for a class of inverse quadratic programming problems. Appl Math Optim. 2010;61:57–83.CrossRef
Metadaten
Titel
A Gradient-Based Neural Network Method for Solving Strictly Convex Quadratic Programming Problems
verfasst von
Alireza Nazemi
Masoomeh Nazemi
Publikationsdatum
01.09.2014
Verlag
Springer US
Erschienen in
Cognitive Computation / Ausgabe 3/2014
Print ISSN: 1866-9956
Elektronische ISSN: 1866-9964
DOI
https://doi.org/10.1007/s12559-014-9249-0

Weitere Artikel der Ausgabe 3/2014

Cognitive Computation 3/2014 Zur Ausgabe

EditorialNotes

Special Issue on ICONIP 2012

OriginalPaper

A Class Incremental Extreme Learning Machine for Activity Recognition

OriginalPaper

Exploiting a Modified Gray Model in Back Propagation Neural Networks for Enhanced Forecasting

OriginalPaper

Scanpath Generated by Cue-Driven Activation and Spatial Strategy: A Comparative Study

OriginalPaper

Multitask Extreme Learning Machine for Visual Tracking

OriginalPaper

A Two-Stage Methodology Using K-NN and False-Positive Minimizing ELM for Nominal Data Classification