In this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is concerned.Using the KKT optimality conditions of the lower level problem,this kind of pr...In this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is concerned.Using the KKT optimality conditions of the lower level problem,this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization problem.Then,a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is introduced.It is shown that the Pareto optimal solutions(stationary points)of the approximate problems converge to a Pareto optimal solution(stationary point)of the original bilevel multiobjective programming problem.Numerical results showing the viability of the smoothing approach are reported.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11201039,71171150,and 61273179).
文摘In this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is concerned.Using the KKT optimality conditions of the lower level problem,this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization problem.Then,a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is introduced.It is shown that the Pareto optimal solutions(stationary points)of the approximate problems converge to a Pareto optimal solution(stationary point)of the original bilevel multiobjective programming problem.Numerical results showing the viability of the smoothing approach are reported.
