Abstract:

Bilevel programming has been widely applied to economics, transportation, ecology, engineering and other fields. At present, the research of bilevel programming is mainly based on the strong bilevel programming and the weak bilevel programming. However, there are few studies on the solution methods to the weak bilevel programming. In this paper, we present a global optimization method for solving the weak linear bilevel programming problems (WLBPP). We first give the relations between the WLBPP and its relaxation problem with respect to their optimal solutions. Using the dual theory of linear programming and penalty function method, we then discuss the relations between the relaxation problem and its penalized problem. Furthermore, we develop a global optimization method, whose advantage is that it only requires solving several linear programming problems to obtain a globally optimal solution of the original problem, for solving the WLBPP. Finally, a simple example illustrates that the proposed method is feasible.

Key words: weak bilevel programming, relaxation problem, penalty function, global optimization method