Name
Title | ||
|---|---|---|
Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization |
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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1287/opre.1110.1014 | Operations Research |
Keywords | DocType | Volume |
piecewise linear multicriteria program,piecewise linear multicriteria programs,continuous case,continuous piecewise linear bi-criteria,ideal point strategy,polyhedron set constraint,discontinuous case,pareto point,linear objective function,discontinuous generalization,continuous linear function,discontinuous bi-criteria portfolio selection,semi-closed polyhedron,piecewise linear function,algorithm | Journal | 60 |
Issue | ISSN | Citations |
2 | 0030-364X | 5 |
PageRank | References | Authors |
0.56 | 20 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ya-ping Fang | 1 | 34 | 2.93 |
| K. W. Meng | 2 | 13 | 2.41 |
| Xiaoqi Yang | 3 | 126 | 20.85 |