Penalty method-based equilibrium point approach for solving the linear bilevel multiobjective programming problem

Abstract

In this paper, a linear bilevel multiobjective programming problem is concerned. Based on the method of replacing the lower level problem with its optimality conditions, and taking the complementary constraints as the penalty term of the upper level objectives, we obtain the exact penalized multiobjective programming problem \begin{document}$ (P_{K}) $\end{document} . The concept of equilibrium point of problem \begin{document}$ (P_{K}) $\end{document} is introduced and its properties are analyzed. Thereafter, we propose a penalty method-based equilibrium point algorithm, which only needs to solve a series of linear programming problems, for the linear bilevel multiobjective programming problem. Numerical results showing viability of the equilibrium point approach are presented.