Combination between global and local methods for solving an optimization problem over the efficient set

In this paper, we propose an algorithm for globally solving optimization problems over efficient sets. The algorithm is established based on a branch and bound scheme in which the bounding procedure is performed by using the well known weak duality theorem in Lagrange duality. A suitable combination of this algorithm with a local search procedure in difference of convex function optimization leads to a promising global algorithm, whose efficiency is more or less confirmed by computational experiments on a large set of test problems.