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Technical Note—Proper Efficiency and the Linear Vector Maximum Problem

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  • H. Isermann

    (University of Regensburg, Regensburg, West Germany)

Abstract

A vector maximum problem arises when more than one scalar-valued objective function is to be maximized simultaneously over a given range of definition. This note considers linear vector maximum problems and shows that each efficient solution of a linear vector maximum problem also satisfies the requirements of a restricted concept of efficiency, the notion of proper efficiency.

Suggested Citation

  • H. Isermann, 1974. "Technical Note—Proper Efficiency and the Linear Vector Maximum Problem," Operations Research, INFORMS, vol. 22(1), pages 189-191, February.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:1:p:189-191
    DOI: 10.1287/opre.22.1.189
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    Cited by:

    1. V. Preda & I. Chiţescu, 1999. "On Constraint Qualification in Multiobjective Optimization Problems: Semidifferentiable Case," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 417-433, February.
    2. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
    3. Eduardo Camponogara & Sarosh N. Talukdar, 2005. "Designing Communication Networks to Decompose Network Control Problems," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 207-223, May.
    4. Alexander Engau, 2017. "Proper Efficiency and Tradeoffs in Multiple Criteria and Stochastic Optimization," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 119-134, January.
    5. Erin K. Doolittle & Hervé L. M. Kerivin & Margaret M. Wiecek, 2018. "Robust multiobjective optimization with application to Internet routing," Annals of Operations Research, Springer, vol. 271(2), pages 487-525, December.
    6. Soylu, Banu, 2018. "The search-and-remove algorithm for biobjective mixed-integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 268(1), pages 281-299.
    7. Siming Pan & Shaokai Lu & Kaiwen Meng & Shengkun Zhu, 2021. "Trade-Off Ratio Functions for Linear and Piecewise Linear Multi-objective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 402-419, February.
    8. Alexander Engau, 2015. "Definition and Characterization of Geoffrion Proper Efficiency for Real Vector Optimization with Infinitely Many Criteria," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 439-457, May.
    9. Jesús A. De Loera & Raymond Hemmecke & Matthias Köppe, 2009. "Pareto Optima of Multicriteria Integer Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 39-48, February.
    10. Anthony Przybylski & Xavier Gandibleux & Matthias Ehrgott, 2010. "A Recursive Algorithm for Finding All Nondominated Extreme Points in the Outcome Set of a Multiobjective Integer Programme," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 371-386, August.
    11. Johannes M. Schumacher, 2018. "A Multi-Objective Interpretation of Optimal Transport," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 94-119, January.
    12. Mehdi Allahdadi & Aida Batamiz, 2021. "Generation of some methods for solving interval multi-objective linear programming models," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1077-1115, December.
    13. Wassila Drici & Fatma Zohra Ouail & Mustapha Moulaï, 2018. "Optimizing a linear fractional function over the integer efficient set," Annals of Operations Research, Springer, vol. 267(1), pages 135-151, August.
    14. Daniel Jornada & V. Jorge Leon, 2020. "Filtering Algorithms for Biobjective Mixed Binary Linear Optimization Problems with a Multiple-Choice Constraint," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 57-73, January.

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