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Pseudo-Concave Programming and Lagrange Regularity

Author

Listed:
  • K. O. Kortanek

    (Cornell University, Ithaca, New York)

  • J. P. Evans

    (Cornell University, Ithaca, New York)

Abstract

For the mathematical programming problem max f ( x ) subject to G ( x ) ≧ 0, we show that if G ( x ) is pseudo-concave, a property weaker than concavity but stronger than quasi-concavity, and differentiable, then the constraint set is necessarily determined by the natural gradient (tangent) inequality system of G . We then apply the duality constructs of semi-infinite programming, in a manner which admits generalizations, to this special case to show that pseudo-concave constraint functions that have an interior point are convex Lagrange regular. Analogous to a theorem of Arrow-Hurwicz-Uzawa, we characterize functions that are both pseudo-concave and pseudo-convex, and for programming problems with objective functions of this form, we obtain equivalent problems having linear objective functions.

Suggested Citation

  • K. O. Kortanek & J. P. Evans, 1967. "Pseudo-Concave Programming and Lagrange Regularity," Operations Research, INFORMS, vol. 15(5), pages 882-891, October.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:5:p:882-891
    DOI: 10.1287/opre.15.5.882
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    Cited by:

    1. Qamrul Hasan Ansari & Mahboubeh Rezaei, 2012. "Invariant Pseudolinearity with Applications," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 587-601, June.
    2. T. Rapcsák & M. Ujvári, 2008. "Some results on pseudolinear quadratic fractional functions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 415-424, December.
    3. S. K. Mishra & B. B. Upadhyay & Le Thi Hoai An, 2014. "Lagrange Multiplier Characterizations of Solution Sets of Constrained Nonsmooth Pseudolinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 763-777, March.
    4. N. T. H. Linh & J.-P. Penot, 2012. "Generalized Affine Functions and Generalized Differentials," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 321-338, August.

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