研究了一类半向量二层规划乐观最优解的求解问题. 利用下层问题的最优性条件构造了该类半向量二层规划问题的罚问题, 分析了原问题的最优解与罚问题最优解之间的关系, 证明了罚函数的精确性. 同时对目标函数和约束条件均为线性函数的半向量二层规划问题研究了其最优性条件, 并设计了相应的罚函数算法. 数值结果表明所设计的罚函数方法对该类半向量二层规划问题是可行的.

In this paper, we are concerned with a class of semivectorial bilevel programming problem. Using the optimality conditions of the lower level programs, we construct the corresponding penalized problem. Then, we analyse the relationships between the optimal solution of the original problem and that of the penalized problem, and prove that the penalty function presented is exact. Then, we analyze the optimality conditions for a special semivectorial bilevel programming problem, where the objective functions and constraints functions are all linear functions. Finally, we propose a penalty function algorithm. The numerical results show that the algorithm is feasible to the semivectorial bilevel programming problem considered.