Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems
Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this paper we propose a new relaxation method for solving multiple objective quadratic programming problems. Exploiting the technique of the linear weighted sum method, we reformulate the original multiple objec...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
20.11.2012
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Subjects | |
Online Access | Get full text |
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Summary: | Multicriterion optimization and Pareto optimality are fundamental tools in
economics. In this paper we propose a new relaxation method for solving
multiple objective quadratic programming problems. Exploiting the technique of
the linear weighted sum method, we reformulate the original multiple objective
quadratic programming problems into a single objective one. Since such single
objective quadratic programming problem is still nonconvex and NP-hard in
general. By using the techniques of lifting and doubly nonnegative relaxation,
respectively, this single objective quadratic programming problem is
transformed to a computable convex doubly nonnegative programming problem. The
optimal solutions of this computable convex problem are (weakly) Pareto optimal
solutions of the original problem under some mild conditions. Moreover, the
proposed method is tested with two examples and a practical portfolio selection
problem. The test problems are solved by \texttt{CVX} package which is a solver
for convex optimization. The numerical results show that the proposed method is
effective and promising. |
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DOI: | 10.48550/arxiv.1211.4670 |