用ε-精确罚函数方法求解非凹两层规划问题  

ε-exact Penalty for Non-concave Bilevel Programming Problems

作　　者：李常敏[1] 朱道立[2] 

机构地区：[1]复旦大学管理学院,上海200433 [2]同济大学经济与管理学院,上海200092

出　　处：《数学物理学报（A辑）》2011年第3期585-593,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(71071035)资助

摘　　要：求解两层规划问题通常的方法是值函数方法和KKT方法,但是对于非凹两层规划问题,这两种方法经常会失效.该文针对非凹规划的情形,通过引进ε-近似解,ε-误差界,利用ε-精确罚函数得到ε-近似单层规划问题,并且证明了其最优解趋近于原问题的最优解.The main tool in the present literature to treat the bilevel programming problems （BLPP） is the method of KKT conditions and value function. However, for the non-concave case, neither technique can be applied. In this paper, the authors introduce the notions of ε-set, ε-error bounds, and use certain ε-uniform error bounds as ε-exact penalties to give single level problems equivalent to the approximate BLPP. Furthermore, they show that any cluster of the approximate sequence is the solution of the BLPP.

关 键 词：非凹两层规划问题 ε-误差界 ε-精确罚函数法 收敛性 

分 类 号：O221.2[理学—运筹学与控制论]