Skip to main content
SpringerLink
Log in

Duality for Nonlinear Programming Problems Involving (b, F) - Convexity

  • Theoretical Papers
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

A new class of convex functions, namely, (b, F)-convex functions is introduced. Sufficient optimality conditions and duality results are established for nonlinear programming problems under (b, F)-convexity assumptions on the functions involved. Further, we extend these results to fractional programming problems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C.R. BECTOR, Mathematical Analysis of some Nonlinear Programming Problems, Indian Institute of Technology, Kanpur, India, Ph.D Thesis, 1968.

    Google Scholar 

  2. C.R. BECTOR, and C. SINGH, B-vex Function, Journal of Optimization Theory and Applications, 71, 237–253 (1991).

    Article  Google Scholar 

  3. C.R. BECTOR, S. SUNEJA, and C. S. LALITHA, Generalized B-vex functions and Generalized B-vex Programming, Journal of Optimization theory and Applications, 76, 651–1576 (1993).

    Article  Google Scholar 

  4. M. A. HANSON and B. MOND, Further generalizations of Convexity in Mathematical Programming, Journal of Information and Optimization Sciences, 3, 25–31 (1982).

    Article  Google Scholar 

  5. O.L. MANGASARIAN, Non-Linear Programming, McGraw Hill, New York, New York, 1969.

    Google Scholar 

  6. D.G. MAHAJAN, and M.N. VARTAK, Generalization of Some Duality Theorems in Nonlinear Programming, Mathematical Programming, 12, 293–317 (1977).

    Article  Google Scholar 

  7. B. MOND, and T. WEIR, Generalized Concavity and Duality, Generalized Concavity in Optimization and Economics (Edited by S. Schaible and W. T. Ziemba), Academic press, New York, pp. 268–279, 1981.

  8. P. WOLFE, A Duality Theorem for Non-linear Programming quarterly Applied Mathematics, 19, 239–244 (1961).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Mepco Schlenk Engg. College Mepco, Nagar -, 626 005, India

    P. Pandian

  2. Department of Mathematics, Gandhigram Rural University, Gandhigram -, 626 032, India

    P. Kanniappan

Authors
  1. P. Pandian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Kanniappan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pandian, P., Kanniappan, P. Duality for Nonlinear Programming Problems Involving (b, F) - Convexity. OPSEARCH 36, 172–180 (1999). https://doi.org/10.1007/BF03398572

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03398572

Search

Navigation