系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2014年
4期
910~916
,共null页
半向量双层规划 多目标规划 偏静态条件 罚函数法
半嚮量雙層規劃 多目標規劃 偏靜態條件 罰函數法
반향량쌍층규화 다목표규화 편정태조건 벌함수법
semivectorial bilevel programming; multi-objective programming; partial calmness; penaltymethod
研究半向量双层规划问题的求解方法．利用Benson’s方法及线性规划问题的对偶理论，将半向量双层规划问题转化为一个单层优化问题，同时提出了转化问题的偏静态条件定义．基于此定义，构造了半向量双层规划的精确罚问题，得到了此类双层规划问题的最优性条件，并给出相应的求解方法．最后通过一个数值例子表明了求解方法的可行性．
研究半嚮量雙層規劃問題的求解方法．利用Benson’s方法及線性規劃問題的對偶理論，將半嚮量雙層規劃問題轉化為一箇單層優化問題，同時提齣瞭轉化問題的偏靜態條件定義．基于此定義，構造瞭半嚮量雙層規劃的精確罰問題，得到瞭此類雙層規劃問題的最優性條件，併給齣相應的求解方法．最後通過一箇數值例子錶明瞭求解方法的可行性．
연구반향량쌍층규화문제적구해방법．이용Benson’s방법급선성규화문제적대우이론，장반향량쌍층규화문제전화위일개단층우화문제，동시제출료전화문제적편정태조건정의．기우차정의，구조료반향량쌍층규화적정학벌문제，득도료차류쌍층규화문제적최우성조건，병급출상응적구해방법．최후통과일개수치례자표명료구해방법적가행성．
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 program- ming 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.
