2003
DOI: 10.1080/0233193031000149894
|View full text |Cite
|
Sign up to set email alerts
|

Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

0
223
0
3

Year Published

2007
2007
2022
2022

Publication Types

Select...
5
3

Relationship

1
7

Authors

Journals

citations
Cited by 416 publications
(226 citation statements)
references
References 321 publications
(252 reference statements)
0
223
0
3
Order By: Relevance
“…In the case where the problem is well-posed, S(x) = {y(x)} for all x ∈ X. As mentioned above, the resulting problem is either investigated in the form (1.1) or kept in the form (1.3) but the assumption is exploited in solution procedures, see [5,7,8,39] for details and related references.…”
Section: S(x)mentioning
confidence: 99%
See 2 more Smart Citations
“…In the case where the problem is well-posed, S(x) = {y(x)} for all x ∈ X. As mentioned above, the resulting problem is either investigated in the form (1.1) or kept in the form (1.3) but the assumption is exploited in solution procedures, see [5,7,8,39] for details and related references.…”
Section: S(x)mentioning
confidence: 99%
“…x ∈ X, y ∈ S(x), (1.3) which is actually designed to handle problems with multiple lower-level solutions. The setvalued mapping S in the latter problem denotes the set of optimal solutions of the lower-level problem (1.2), i.e., precisely, More details on solution methods using explicitly or implicitly imposed well-posedness can be found in [5,7,8,24,30,31,39] and references therein. It is important to note that well-posed problems are naturally advantageous for the leader, but do not reflect most real-world systems, where the reaction of the follower should be based on her/his best interest, whether it suits the upper-level or not.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…The follower makes its decisions after, and in view of, the decisions of the leader. For an overview and references, see [1].…”
Section: Introductionmentioning
confidence: 99%
“…For instance, the linear and the nonlinear but convex bilevel programming problems have been addressed in [4,5,9,12,13,26,27]. A thorough bibliographic review can be found in [10]. On the other hand, general bilevel programming problems with a nonconvex inner problem have received much less attention due to their intrinsic difficulties and currently are only addressed in [21,23].…”
mentioning
confidence: 99%