Is bilevel programming a special case of a mathematical program with complementarity constraints?

By Stephan Dempe, Joydeep Dutta. 2012

264 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Ocean Engineering

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Susanne Franke
2. Truong Quang Bao
3. Boris S. Mordukhovich
4. Stephan Dempe
5. René Vidal
6. Paris V. Giampouras
7. Liangzu Peng
8. Hung M. Phan

In Control and Systems Engineering

1. Boris S. Mordukhovich
2. Truong Quang Bao
3. Susanne Franke
4. Stephan Dempe
5. René Vidal
6. Paris V. Giampouras
7. Liangzu Peng
8. Joydeep Dutta

In Ocean Engineering

1. Truong Quang Bao
2. Boris S. Mordukhovich
3. René Vidal
4. Paris V. Giampouras
5. Liangzu Peng

Citations in the corpus

• The Ideal Continual Learner: An Agent That Never Forgets (2023, methodology): “More generally, a common idea in bilevel programming is to rewrite the lower-level problem (e.g., w ∈ Kt−1) as KKT conditions, and many algorithms exist for the latter formulation; see, e.g., Dempe & Dutta (2012) and the follow-up works.”
• On the solution of convex bilevel optimization problems (2015, background): “Example 4.1 in Dempe and Dutta [25] can be used to show that the (MFCQ) is not a constraint qualification for the lower level problem which is generically satisfied.”
• Set-valued optimization in welfare economics (2010, methodology): “In this vein we mention the classical calculus of variations and optimal control and also models of bilevel programming/Stackelberg games recently illuminated in [ 9 ].”