A Mixed Method For Solving Semivectorial Bilevel Programming Problem

Under the convexity assumption,this paper mainly studies the algorithm problem of optimistic semivectorial bilevel programming.Since the lower level of the semivectorial bilevel programming problem is a multi-objective optimization problem,it is difficult to obtain the absolute optimal solution.Therefore,it is hoped that the equilibrium among the lower level decision makers can be achieved,and making them relatively satisfied under the most unfavorable conditions.In this paper,a hybrid algorithm for solving semivectorial bilevel programming problem is proposed.On the basis of the original scaling method,based on the min-max method of multi-objective programming,an objective is added to the lower level,which is transformed into a bilevel programming problem of two-objective parametric programming at the lower level,and then scaled to a single-objective bilevel programming problem.Finally,the KKT condition is used to transform it into an MPEC problem for solution.The numerical experiments show that the hybrid algorithm is feasible for solving this kind of semivectorial bilevel programming problem.