Solution of bilevel optimization problems using the KKT approach

ABSTRACT

Using the Karush–Kuhn–Tucker conditions for the convex lower level problem, the bilevel optimization problem is transformed into a single-level optimization problem (a mathematical program with complementarity constraints). A regularization approach for the latter problem is formulated which can be used to solve the bilevel optimization problem. This is verified if global or local optimal solutions of the auxiliary problems are computed. Stationary solutions of the auxiliary problems converge to C-stationary solutions of the mathematical program with complementarity constraints.

KEYWORDS:

• Bilevel optimization
• Karush–Kuhn–Tucker transformation
• mathematical program with complementarity constraints

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C26
• 91A65
• 65K05

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

S. Dempe http://orcid.org/0000-0001-6344-5152

Additional information

Funding

Research of both authors has been supported by Deutsche Forschungsgemeinschaft [grant number DE 650/7-1].