Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Saddle Point Criteria in Nonsmooth Semi-Infinite Minimax Fractional Programming Problems

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper considers a nonsmooth semi-infinite minimax fractional programming problem (SIMFP) involving locally Lipschitz invex functions. The authors establish necessary optimality conditions for SIMFP. The authors establish the relationship between an optimal solution of SIMFP and saddle point of scalar Lagrange function for SIMFP. Further, the authors study saddle point criteria of a vector Lagrange function defined for SIMFP.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Vaz A, Ismael F, Fernandes Edite M G P, and Gomes M, Paula S F, Robot trajectory planning with semi-infinite programming, EURO young scientists-papers from the EURO Peripatetic Post-Graduate Programme (Paris,2001), European J. Oper. Res., 2004, 153(2): 607–617.

    Article  MathSciNet  MATH  Google Scholar 

  2. Tong X, Ling C, and Qi L, A semi-infinite programming algorithm for solving optimal power flow with transient stability constraints, J. Comput. Appl. Math., 2008, 217(2): 432–447.

    Article  MathSciNet  MATH  Google Scholar 

  3. Vaz A, Ismael F, and Ferreira Eugnio C, Air pollution control with semi-infinite programming, Appl. Math. Model., 2009, 33(4): 1957–1969.

    Article  MathSciNet  MATH  Google Scholar 

  4. Winterfeld A, Application of general semi-infinite programming to lapidary cutting problems, European J. Oper. Res., 2008, 191(3): 838–854.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bagirov A, Karmitsa N, and Mäkelä M M, Introduction to Nonsmooth Optimization: Theory, Practice and Software, Springer, Heidelberg, New York, Dordrecht, London, 2014.

    Book  MATH  Google Scholar 

  6. Kanzi N and Nobakhtian S, Nonsmooth semi-infinite programming problems with mixed constraints, J. Math. Anal. Appl., 2009, 351(1): 170–181.

    Article  MathSciNet  MATH  Google Scholar 

  7. Zalmai G J and Zhang Q H, Optimality conditions and duality in nonsmooth semi infinite programming, Numer. Funct. Anal. Optim., 2012, 33(4): 452–472.

    Article  MathSciNet  MATH  Google Scholar 

  8. Li Z F and Wang S Y, Lagrange multipliers and saddle points in multiobjective programming, J. Optim. Theory Appl., 1984, 83: 63–81.

    Article  MathSciNet  MATH  Google Scholar 

  9. Mangasarian O L, Nonlinear programming, corrected reprint of the 1969 original, Classics Appl. Math., Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994, 10.

    Google Scholar 

  10. Sawaragi Y, Nakayama H, and Tanino T, Theory of Multiobjective Optimization, Academic Press. Inc. Orlando, 1985.

    MATH  Google Scholar 

  11. Yu P L, Multiple-Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York, 1985.

    Book  Google Scholar 

  12. Xu Z K, Saddle-point type optimality criteria for generalized fractional programming, J. Optim. Theory Appl., 1988, 57(1): 189–196.

    Article  MathSciNet  MATH  Google Scholar 

  13. Lopez M A and Vercher E, Optimality conditions for nondifferentiable convex semiinfinite programming, Math. Program., 1983, 27: 307–319.

    Article  MATH  Google Scholar 

  14. Antczak T, Parametric saddle point criteria in semi-infinite minimax fractional programming problems under (p,r)-invexity, Num. Func. Anal. Optim., 1983, 36: 1–28.

    MathSciNet  MATH  Google Scholar 

  15. Clarke F H, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.

    MATH  Google Scholar 

  16. Reiland T W, Nonsmooth invexity, Bull. Aust. Math. Soc., 1990, 42: 437–446.

    Article  MathSciNet  MATH  Google Scholar 

  17. Goberna M A and Lopez M A, Linear Semi-Infinite Optimazation, Wiley, Chichester, 1987.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    S. K. Mishra & Yadvendra Singh

  2. Department of Mathematics, Texas State University, Texas, USA

    R. U. Verma

Authors
  1. S. K. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yadvendra Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. U. Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. K. Mishra.

Additional information

The paper was supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India under Grant No. 09/013(0474)/2012-EMR-1.

This paper was recommended for publication by Editor WANG Shouyang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mishra, S.K., Singh, Y. & Verma, R.U. Saddle Point Criteria in Nonsmooth Semi-Infinite Minimax Fractional Programming Problems. J Syst Sci Complex 31, 446–462 (2018). https://doi.org/10.1007/s11424-017-6085-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-017-6085-9

Keywords

Search

Navigation