Saddle points and scalarizing sets in multiple objective linear programming - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematical Methods of Operations Research Année : 2014

Saddle points and scalarizing sets in multiple objective linear programming

Résumé

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.
Fichier non déposé

Dates et versions

hal-01509886 , version 1 (18-04-2017)

Identifiants

Citer

Daniel Gourion, The Luc Dinh. Saddle points and scalarizing sets in multiple objective linear programming. Mathematical Methods of Operations Research, 2014, 80 (1), pp.1-27. ⟨10.1007/s00186-014-0467-8⟩. ⟨hal-01509886⟩
106 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More