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Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming

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  • T. Illés

    (Eötvös Loránd University)

  • G. Kassay

    (Babeş-Bolyai University)

Abstract

A general alternative theorem for convexlike functions is given. This permits the establishment of optimality conditions for convexlike programming problems in which both inequality and equality constraints are considered. It is shown that the main results of the paper contain, in particular, those of Craven, Giannessi, Jeyakumar, Hayashi, and Komiya, Simons, Zălinescu, and a recent result of Tamminen.

Suggested Citation

  • T. Illés & G. Kassay, 1999. "Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 243-257, May.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:2:d:10.1023_a:1021781308794
    DOI: 10.1023/A:1021781308794
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    References listed on IDEAS

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    1. Illés, T. & Kassay, G., 1994. "Farkas type theorems for generalized convexities," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 5(2), pages 225-239.
    2. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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    Cited by:

    1. Manh Hung Nguyen & Do Van Luu, 2006. "On constraint qualifications with generalized convexity and optimality conditions," Cahiers de la Maison des Sciences Economiques b06020, Université Panthéon-Sorbonne (Paris 1).
    2. Frenk, J.B.G. & Kassay, G. & Kolumban, J., 2002. "Equivalent Results in Minimax Theory," ERIM Report Series Research in Management ERS-2002-08-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. P. H. Sach, 2007. "Moreau–Rockafellar Theorems for Nonconvex Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 213-227, May.
    4. Adan, M. & Novo, V., 2003. "Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness," European Journal of Operational Research, Elsevier, vol. 149(3), pages 641-653, September.
    5. Frenk, J. B. G. & Kassay, G. & Kolumban, J., 2004. "On equivalent results in minimax theory," European Journal of Operational Research, Elsevier, vol. 157(1), pages 46-58, August.
    6. Do Van Luu & Manh-Hung Nguyen, 2006. "On alternative theorems and necessary conditions for efficiency," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00112454, HAL.
    7. Jiawei Chen & Elisabeth Köbis & Jen-Chih Yao, 2019. "Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 411-436, May.
    8. P. Montiel López & M. Ruiz Galán, 2016. "Nonlinear Programming via König’s Maximum Theorem," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 838-852, September.
    9. J.B.G. Frenk & G. Kassay & J. Kolumbán, 2002. "Equivalent Results in MinimaxTheory," Tinbergen Institute Discussion Papers 02-009/4, Tinbergen Institute.
    10. M. Ruiz Galán, 2016. "A sharp Lagrange multiplier theorem for nonlinear programs," Journal of Global Optimization, Springer, vol. 65(3), pages 513-530, July.

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