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Convexifactors, Generalized Convexity, and Optimality Conditions

Author

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  • J. Dutta

    (Indian Statistical Institute)

  • S. Chandra

    (Indian Institute of Technology)

Abstract

The recently introduced notion of a convexifactor is further studied, and quasiconvex and pseudoconvex functions are characterized in terms of convexifactors. As an application to a chain rule, a necessary optimality condition is deduced for an inequality constrained mathematical programming problem.

Suggested Citation

  • J. Dutta & S. Chandra, 2002. "Convexifactors, Generalized Convexity, and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 41-64, April.
    • Handle: RePEc:spr:joptap:v:113:y:2002:i:1:d:10.1023_a:1014853129484
    DOI: 10.1023/A:1014853129484
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    References listed on IDEAS

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    1. V. Jeyakumar & D. T. Luc, 1999. "Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 599-621, June.
    2. D. Aussel, 1998. "Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 29-45, April.
    3. J. P. Penot & P. H. Sach, 1997. "Generalized Monotonicity of Subdifferentials and Generalized Convexity," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 251-262, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. S. K. Suneja & B. Kohli, 2011. "Optimality and Duality Results for Bilevel Programming Problem Using Convexifactors," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 1-19, July.
    2. Balendu Bhooshan Upadhyay & Shubham Kumar Singh & Ioan Stancu-Minasian, 2024. "Constraint Qualifications and Optimality Conditions for Nonsmooth Semidefinite Multiobjective Programming Problems with Mixed Constraints Using Convexificators," Mathematics, MDPI, vol. 12(20), pages 1-21, October.
    3. X. F. Li & J. Z. Zhang, 2006. "Necessary Optimality Conditions in Terms of Convexificators in Lipschitz Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 429-452, December.
    4. A. Kabgani & F. Lara, 2023. "Semistrictly and neatly quasiconvex programming using lower global subdifferentials," Journal of Global Optimization, Springer, vol. 86(4), pages 845-865, August.
    5. Alireza Kabgani, 2021. "Characterization of Nonsmooth Quasiconvex Functions and their Greenberg–Pierskalla’s Subdifferentials Using Semi-Quasidifferentiability notion," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 666-678, May.
    6. Do Luu, 2014. "Necessary and Sufficient Conditions for Efficiency Via Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 510-526, February.
    7. X. F. Li & J. Z. Zhang, 2010. "Existence and Boundedness of the Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 373-386, May.
    8. Alireza Kabgani & Majid Soleimani-damaneh & Moslem Zamani, 2017. "Optimality conditions in optimization problems with convex feasible set using convexificators," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 103-121, August.
    9. Bhawna Kohli, 2012. "Optimality Conditions for Optimistic Bilevel Programming Problem Using Convexifactors," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 632-651, March.

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