用ε-精确罚函数方法求解非凹两层规划问题

Abstract

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

CLC Number:

90C26

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LI Chang-Min, ZHU Dao-Li. ε-exact Penalty for Non-concave Bilevel Programming Problems[J].Acta mathematica scientia,Series A, 2011, 31(3): 585-593.

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ε-exact Penalty for Non-concave Bilevel Programming Problems

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