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Invariant Pseudolinearity with Applications

Author

Listed:
  • Qamrul Hasan Ansari

    (Aligarh Muslim University)

  • Mahboubeh Rezaei

    (University of Isfahan)

Abstract

In this paper, we introduce the notion of invariant pseudolinearity for nondifferentiable and nonconvex functions by means of Dini directional derivatives. We present some characterizations of invariant pseudolinear functions. Some characterizations of the solution set of a nonconvex and nondifferentiable, but invariant, pseudolinear program are obtained. The results of this paper extend various results for pseudolinear functions, pseudoinvex functions, and η-pseudolinear functions, and also for pseudoinvex programs, pseudolinear programs, and η-pseudolinear programs.

Suggested Citation

  • Qamrul Hasan Ansari & Mahboubeh Rezaei, 2012. "Invariant Pseudolinearity with Applications," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 587-601, June.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:3:d:10.1007_s10957-011-9979-z
    DOI: 10.1007/s10957-011-9979-z
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    References listed on IDEAS

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    2. X. M. Yang, 2009. "On Characterizing the Solution Sets of Pseudoinvex Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 537-542, March.
    3. C. S. Lalitha & Monika Mehta, 2007. "A Note On Pseudolinearity In Terms Of Bifunctions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(01), pages 83-91.
    4. Schaible, Siegfried & Ibaraki, Toshidide, 1983. "Fractional programming," European Journal of Operational Research, Elsevier, vol. 12(4), pages 325-338, April.
    5. Giorgio Giorgi & Sándor Komlósi, 1995. "Dini derivatives in optimization — Part III," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 18(1), pages 47-63, March.
    6. K. O. Kortanek & J. P. Evans, 1967. "Pseudo-Concave Programming and Lagrange Regularity," Operations Research, INFORMS, vol. 15(5), pages 882-891, October.
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