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Saddle points and scalarizing sets in multiple objective linear programming

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  • Daniel Gourion
  • Dinh Luc

Abstract

The main purpose of this paper is to study saddle points of the vector Lagrangian function associated with a multiple objective linear programming problem. We introduce three concepts of saddle points and establish their characterizations by solving suitable systems of equalities and inequalities. We deduce dual programs and prove a relationship between saddle points and dual solutions, which enables us to obtain an explicit expression of the scalarizing set of a given saddle point in terms of normal vectors to the value set of the problem. Finally, we present an algorithm to compute saddle points associated with non-degenerate vertices and the corresponding scalarizing sets. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Daniel Gourion & Dinh Luc, 2014. "Saddle points and scalarizing sets in multiple objective linear programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 1-27, August.
    • Handle: RePEc:spr:mathme:v:80:y:2014:i:1:p:1-27
    DOI: 10.1007/s00186-014-0467-8
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    References listed on IDEAS

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    1. Luc, Dinh The, 2011. "On duality in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 210(2), pages 158-168, April.
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    Cited by:

    1. Nguyen Xuan Hai & Nguyen Hong Quan & Vo Viet Tri, 2023. "Some saddle-point theorems for vector-valued functions," Journal of Global Optimization, Springer, vol. 86(1), pages 141-161, May.

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