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Generalized Affine Functions and Generalized Differentials

Author

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  • N. T. H. Linh

    (International University, Vietnam National University at Ho Chi Minh City)

  • J.-P. Penot

    (Université Pierre et Marie Curie)

Abstract

We study some classes of generalized affine functions, using a generalized differential. We study some properties and characterizations of these classes and we devise some characterizations of solution sets of optimization problems involving such functions or functions of related classes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:2:d:10.1007_s10957-012-0051-4
    DOI: 10.1007/s10957-012-0051-4
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    References listed on IDEAS

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    1. J.P. Penot, 2003. "Lagrangian Approach to Quasiconvex Programing," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 637-647, June.
    2. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    3. M. Bianchi & S. Schaible, 2000. "An Extension of Pseudolinear Functions and Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 59-71, January.
    4. Komlosi, S., 1993. "First and second order characterizations of pseudolinear functions," European Journal of Operational Research, Elsevier, vol. 67(2), pages 278-286, June.
    5. J.P. Penot, 2003. "Characterization of Solution Sets of Quasiconvex Programs," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 627-636, June.
    6. K. O. Kortanek & J. P. Evans, 1967. "Pseudo-Concave Programming and Lagrange Regularity," Operations Research, INFORMS, vol. 15(5), pages 882-891, October.
    Full references (including those not matched with items on IDEAS)

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