Saddle points and scalarizing sets in multiple objective linear programming

Daniel Gourion () and Dinh Luc

Mathematical Methods of Operations Research, 2014, vol. 80, issue 1, 27 pages

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

Keywords: Multiple objective linear problem; Vector Lagrangian function; Saddle point; Duality; Scalarizing set; 90C31 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s00186-014-0467-8

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