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Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

Author

Listed:
  • G. Z. Ruan

    (Xiangtan University)

  • S. Y. Wang

    (Chinese Academy of Sciences
    Hunan University)

  • Y. Yamamoto

    (University of Tsukuba)

  • S. S. Zhu

    (Chinese Academy of Sciences
    Fudan University)

Abstract

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.

Suggested Citation

  • G. Z. Ruan & S. Y. Wang & Y. Yamamoto & S. S. Zhu, 2004. "Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 409-429, November.
    • Handle: RePEc:spr:joptap:v:123:y:2004:i:2:d:10.1007_s10957-004-5156-y
    DOI: 10.1007/s10957-004-5156-y
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    References listed on IDEAS

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    3. Amouzegar, Mahyar A. & Moshirvaziri, Khosrow, 1999. "Determining optimal pollution control policies: An application of bilevel programming," European Journal of Operational Research, Elsevier, vol. 119(1), pages 100-120, November.
    4. Bard, Jonathan F., 1985. "Geometric and algorithmic developments for a hierarchical planning problem," European Journal of Operational Research, Elsevier, vol. 19(3), pages 372-383, March.
    5. Jonathan F. Bard, 1983. "An Algorithm for Solving the General Bilevel Programming Problem," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 260-272, May.
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    Cited by:

    1. Armita Khorsandi & Bing-Yuan Cao & Hadi Nasseri, 2019. "A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    2. Nuno Faísca & Pedro Saraiva & Berç Rustem & Efstratios Pistikopoulos, 2009. "A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems," Computational Management Science, Springer, vol. 6(4), pages 377-397, October.

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