On computing objective function values in multiple objective quadratic–linear programming

In this paper, we will consider the computation of objective function values when a nondominated frontier is searched in multiple objective quadratic–linear programming. Reference directions and weighted-sums constitute a methodological basis for the search. This idea leads to a parametric linear complementarity model formulation. A critical task of making a search procedure efficient is to compute the changes in quadratic and linear objective functions efficiently when a search direction is changed or a basis change is performed. Those changes in objective functions can be computed by a so-called direct or indirect method. The direct method is a straightforward one and based on the use of unit changes in basic decision variables. Instead, the indirect method utilizes some other basic variables of the model. We will introduce the indirect method and make theoretical and empirical comparisons between the methods. Based on the comparisons, we point out that the indirect method is clearly much more efficient than the direct one.