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Multicriterion optimization and Pareto optimality are fundamental tools ineconomics. In this paper we propose a new relaxation method for solvingmultiple objective quadratic programming problems. Exploiting the technique ofthe linear weighted sum method, we reformulate the original multiple objectivequadratic programming problems into a single objective one. Since such singleobjective quadratic programming problem is still nonconvex and NP-hard ingeneral. By using the techniques of lifting and doubly nonnegative relaxation,respectively, this single objective quadratic programming problem istransformed to a computable convex doubly nonnegative programming problem. Theoptimal solutions of this computable convex problem are (weakly) Pareto optimalsolutions of the original problem under some mild conditions. Moreover, theproposed method is tested with two examples and a practical portfolio selectionproblem. The test problems are solved by \texttt{CVX} package which is a solverfor convex optimization. The numerical results show that the proposed method iseffective and promising.

Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems