关键词: 非凹两层规划问题,  &epsilon, -误差界,  &epsilon, -精确罚函数法, 收敛性

Abstract:

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.

Key words: Non-concave bilevel programming problems,  ε-error bound,  ε-exact penalty, Convergence