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This paper considered the semivectorial bilevel programming problem. By using Benson's method and dual theory of linear programming, the original problem was transformed into a single level optimization problem. This paper gave a definition of partial calmness of the transformed problem. Based on this definition, this paper constructed an exact penalized problem of the semivectorial bilevel programming problem, gave its optimality condition, and proposed an algorithm to solve it. Finally, this paper gave a numerical example to show that the algorithm is feasible. [ABSTRACT FROM AUTHOR]