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On Convex Generalized Systems

Author

Listed:
  • G. Mastroeni

    (Universitá di Pisa)

  • T. Rapcsák

    (Hungarian Academy of Sciences)

Abstract

In this paper, the set-convexity and mapping-convexity properties of the extended images of generalized systems are considered. By using these image properties and tools of topological linear spaces, separation schemes ensuring the impossibility of generalized systems are developed. Then, special problem classes are investigated.

Suggested Citation

  • G. Mastroeni & T. Rapcsák, 2000. "On Convex Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 605-627, March.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:3:d:10.1023_a:1004641726264
    DOI: 10.1023/A:1004641726264
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    References listed on IDEAS

    as
    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.
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    Cited by:

    1. J. B. G. Frenk & G. Kassay, 2007. "Lagrangian Duality and Cone Convexlike Functions," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 207-222, August.
    2. Jun Li & Giandomenico Mastroeni, 2018. "Refinements on Gap Functions and Optimality Conditions for Vector Quasi-Equilibrium Problems via Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 696-716, June.
    3. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 609-636, June.
    4. Frenk, J.B.G. & Kassay, G., 2005. "Lagrangian duality and cone convexlike functions," ERIM Report Series Research in Management ERS-2005-019-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.
    5. J. Li & L. Yang, 2018. "Set-Valued Systems with Infinite-Dimensional Image and Applications," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 868-895, December.

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