A discretization iteration approach for solving a class of semivectorial bilevel programming problem

The pessimistic optimal solution of the semivectorial bilevel programming problem with no upper level variables in the lower level constraints is concerned. Based on the scalarization techniques and optimal value transforming approach for the lower level problem, the semivectorial bilevel programming problem is transformed into the corresponding infinite-dimensional optimization problem. Then, a discretization iterative algorithm is proposed, and the convergence of the algorithm is also analyzed. The numerical results show that the algorithm is feasible for the pessimistic optimal solution of the semivectorial bilevel programming problem studied.