A reference direction approach to multiple objective quadratic–linear programming

In this paper, we propose an interactive procedure for solving multiple criteria problems with one quadratic objective, several linear objectives, and a set of linear constraints. The procedure is based on the use of reference directions and weighted sums. Reference directions for the linear functions, and weighted sums for combining the quadratic function with the linear ones are used as parameters to implement the free search of nondominated solutions. The idea leads to the parametric linear complementarity problem formulation. An approach to deal with this type of problems is given as well. The approach is illustrated with a numerical example.