Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/30681
Title: Piecewise linear multicriteria programs : the continuous case and its discontinuous generalization
Authors: Fang, YP
Meng, K
Yang, XQ 
Keywords: Algorithm
Bi-criteria program
Multicriteria program
Piecewise linear function
The structure of (weak) Pareto solution set
Issue Date: 2012
Publisher: Institute for Operations Research and the Management Sciences
Source: Operations research, 2012, v. 60, no. 2, p. 398-409 How to cite?
Journal: Operations research 
Abstract: In this paper we study piecewise linear multicriteria programs, that is, multicriteria programs with either a continuous or discontinuous piecewise linear objective function and a polyhedron set constraint. We obtain an algebraic representation of a semi-closed polyhedron and apply it to show that the image of a semi-closed polyhedron under a continuous linear function is always one semi-closed polyhedron. We establish that the (weak) Pareto solution/point set of a piecewise linear multicriteria program is the union of finitely many semi-closed polyhedra. We propose an algorithm for finding the Pareto point set of a continuous piecewise linear bi-criteria program and generalize it to the discontinuous case. We apply our algorithm to solve the discontinuous bi-criteria portfolio selection problem with an l ∞ risk measure and transaction costs and show that this algorithm can be improved by using an ideal point strategy.
URI: http://hdl.handle.net/10397/30681
ISSN: 0030-364x
EISSN: 1526-5463
DOI: 10.1287/opre.1110.1014
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