Characterization of approximately efficient solutions to multiobjective location problems using Ekeland's variational principle

The paper deals with multiobjective location problems of the so-called point-objective type with linear inequality restrictions and additional linear terms in the objective functions and linear operators in the norm parts. If the latter ones are replaced by the identity mapping one obtains the usual point-objective location problem. Approximately efficient solutions are considered for these problems. Using a vectorial variational principle a slightly perturbed multicriterial location problem is derived which is investigated with respect to duality. A dual vectorial optimization problem is established and weak and strong duality assertions are derived. By means of the duality results optimality conditions for the perturbed location problem are obtained. The optimality conditions are then applied to get characterizing conditions for approximately efficient solutions to the original multiobjective location problem.