Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 20, Issue 4, Pages 1885-1905Publisher
SIAM PUBLICATIONS
DOI: 10.1137/080725088
Keywords
necessary optimality conditions; partial calmness; constraint qualifications; nonsmooth analysis; value function; bilevel programming problems
Categories
Funding
- NSERC
- National Natural Science Foundation of China, NSFC
Ask authors/readers for more resources
The bilevel program is a sequence of two optimization problems where the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. The classical approach to solving such a problem is to replace the lower level problem by its Karush-Kuhn-Tucker (KKT) condition and solve the resulting mathematical programming problem with equilibrium constraints (MPEC). In general the classical approach is not valid for nonconvex bilevel programming problems. The value function approach uses the value function of the lower level problem to define an equivalent single level problem. But the resulting problem requires a strong assumption, such as the partial calmness condition, for the KKT condition to hold. In this paper we combine the classical and the value function approaches to derive new necessary optimality conditions under rather weak conditions. The required conditions are even weaker in the case where the classical approach or the value function approach alone is applicable.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available