[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

Newton Like Line Search Method Using q-Calculus

  • Conference paper
  • First Online:
Mathematics and Computing (ICMC 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 655))

Included in the following conference series:

Abstract

In this paper some Newton like methods for unconstrained optimization problem are restructured using q-calculus (quantum calculus). Two schemes are proposed, (1) q-Newton line search scheme, (2) a variant of q-Newton line search scheme. Global convergence of these schemes are discussed and numerical illustrations are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 35.99
Price includes VAT (United Kingdom)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 44.99
Price includes VAT (United Kingdom)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Abreu, L.: A q-sampling theorem related to the q-Hankel transform. Proc. Am. Math. Soc. 133(4), 1197–1203 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aral, A., Gupta, V., Agarwal, R.P.: Applications of q-Calculus in Operator Theory. Springer, New York (2013)

    Book  MATH  Google Scholar 

  3. Bangerezako, G.: Variational q-calculus. J. Math. Anal. Appl. 289(2), 650–665 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bunch, J.R., Kaufman, L., Parlett, B.N.: Decomposition of a symmetric matrix. Numer. Math. 27(1), 95–109 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  5. Duff, I.S., Reid, J.K.: The multifrontal solution of indefinite sparse symmetric linear. ACM Trans. Math. Softw. (TOMS) 9(3), 302–325 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fourer, R., Mehrotra, S.: Solving symmetric indefinite systems in an interior-point method for linear programming. Math. Program. 62(1–3), 15–39 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gauchman, H.: Integral inequalities in q-calculus. Comput. Math. Appl. 47(2), 281–300 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Golub, G.H., Van Loan, C.F.: Matrix Computations, vol. 3. JHU Press, Baltimore (2012)

    MATH  Google Scholar 

  9. Grünbaum, F.A., Haine, L.: The q-version of a theorem of bochner. J. Comput. Appl. Math. 68(1), 103–114 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ismail, M.E., Stanton, D.: Applications of q-Taylor theorems. J. Comput. Appl. Math. 153(1), 259–272 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jing, S.C., Fan, H.Y.: q-Taylor’s formula with its q-remainder. Commun. Theor. Phys. 23(1), 117 (1995)

    Article  MathSciNet  Google Scholar 

  12. Koornwinder, T.H., Swarttouw, R.F.: On q-analogues of the Fourier and Hankel transforms. Trans. Am. Math. Soc. 333(1), 445–461 (1992)

    MathSciNet  MATH  Google Scholar 

  13. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research and Financial Engineering, 2nd edn. Springer, New York (2006)

    MATH  Google Scholar 

  14. Rajkovic, P.M., Marinkovi, S.D., Stankovic, M.S.: Fractional integrals and derivatives in q-calculus. Appl. Anal. Discrete Math. 1(1), 311–323 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rajkovic, P.M., Marinkovic, S.D., Stankovic, M.S.: On q-Newton Kantorovich method for solving systems of equations. Appl. Math. Comput. 168(2), 1432–1448 (2005)

    MathSciNet  MATH  Google Scholar 

  16. Rajkovic, P.M., Stankovic, M.S., Marinkovic, S.D.: Mean value theorems in q-calculus. Matematicki Vesnik 54, 171–178 (2002)

    MathSciNet  MATH  Google Scholar 

  17. Soterroni, A.C., Galski, R.L., Ramos, F.M.: The q-gradient vector for unconstrained continuous optimization problems. In: Hu, B., Morasch, K., Pickl, S., Siegle, M. (eds.) Operations Research Proceedings 2010, pp. 365–370. Springer, Heidelberg (2011). doi:10.1007/978-3-642-20009-0_58

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Suvra Kanti Chakraborty .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Nature Singapore Pte Ltd.

About this paper

Cite this paper

Chakraborty, S.K., Panda, G. (2017). Newton Like Line Search Method Using q-Calculus. In: Giri, D., Mohapatra, R., Begehr, H., Obaidat, M. (eds) Mathematics and Computing. ICMC 2017. Communications in Computer and Information Science, vol 655. Springer, Singapore. https://doi.org/10.1007/978-981-10-4642-1_17

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-4642-1_17

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4641-4

  • Online ISBN: 978-981-10-4642-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics