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Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems

Author

Listed:
  • R. Zeng

    (Chongqing Normal University
    Saskatchewan Institute of Applied Science and Technology)

  • R. J. Caron

    (Saskatchewan Institute of Applied Science and Technology)

Abstract

In this paper, we introduce a definition of generalized convexlike functions (preconvexlike functions). Then, under the weakened convexity, we study vector optimization problems in Hausdorff topological linear spaces. We establish some generalized Motzkin theorems of the alternative. By use of these theorems of the alternative, we obtain some Lagrangian multiplier theorems. A saddle-point theorem and a scalarization theorem are also derived.

Suggested Citation

  • R. Zeng & R. J. Caron, 2006. "Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 281-299, November.
    • Handle: RePEc:spr:joptap:v:131:y:2006:i:2:d:10.1007_s10957-006-9140-6
    DOI: 10.1007/s10957-006-9140-6
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    References listed on IDEAS

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    1. X. M. Yang & X. Q. Yang & G. Y. Chen, 2000. "Theorems of the Alternative and Optimization with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 627-640, December.
    2. J. Gwinner & W. Oettli, 1994. "Theorems of the Alternative and Duality for INF-SUP Problems," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 238-256, February.
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    Cited by:

    1. Fabián Flores-Bazán & Giandomenico Mastroeni & Cristián Vera, 2019. "Proper or Weak Efficiency via Saddle Point Conditions in Cone-Constrained Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 787-816, June.
    2. J. Li & G. Mastroeni, 2016. "Image Convexity of Generalized Systems with Infinite-Dimensional Image and Applications," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 91-115, April.
    3. Hachem Slimani & Mohammed-Said Radjef, 2016. "Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints," Operational Research, Springer, vol. 16(2), pages 349-364, July.

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