Solving linear bilevel multiobjective programming problem via exact penalty function approach

In this paper, the linear bilevel multiobjective programming problem is addressed. The duality gap of the lower level problem is appended to the objectives of the upper level problem with a penalty, and a penalized problem for the linear bilevel multiobjective programming problem is obtained. We prove that the Pareto optimality is reached for an exact penalty function, then an algorithm (original algorithm) is proposed. In addition, for the linear bilevel multiobjective programming problem with given weights for the upper level objective functions, we analyze the optimality conditions and propose an algorithm (weights algorithm). The numerical results showing viability of the penalty function approach are presented.