A BOUNDING APPROACH FOR THE OPTIMISTIC OPTIMAL SOLUTION OF A CLASS OF SEMIVECTORIAL BILEVEL PROGRAMMING PROBLEM

For the semivectorial bilevel programming problem, where the lower level is a convex vector optimization problem, based on the optimal value transformation approach for the lower level problem, a bounding algorithm is proposed. The lower bounding problem is obtained by relaxing the constraints containing the parametric optimal solution value function of the lower level problem, and the upper bounding problem is obtained by probing some feasible points. The algorithm can terminate finitely to a e-optimality point of the upper and the lower level programs and the numerical results illustrating the bounding algorithm are also presented.