Optimality conditions for bilevel programming problems

DOI10.1080/02331930600816189zbMath1156.90457OpenAlexW4236995599MaRDI QIDQ5898677

Joydeep Dutta, Sebastian Lohse, Stephan Dempe

Publication date: 8 March 2007

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930600816189

zbMATH Keywords

necessary and sufficient optimality conditionsbilevel programming

Mathematics Subject Classification ID

Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46)

Related Items

Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market ⋮ Finding optimal strategies in a multi-period multi-leader-follower Stackelberg game using an evolutionary algorithm ⋮ Approximated set-valued mapping approach for handling multiobjective bilevel problems ⋮ A projected subgradient algorithm for bilevel equilibrium problems and applications ⋮ The generalized Mangasarian-Fromowitz constraint qualification and optimality conditions for bilevel programs ⋮ On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problem ⋮ Optimality Conditions for a Simple Convex Bilevel Programming Problem ⋮ Unnamed Item ⋮ Evolutionary algorithm for bilevel optimization using approximations of the lower level optimal solution mapping ⋮ Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

Cites Work

• Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints
• Maximum principle in the problem of time optimal response with nonsmooth constraints
• Complementarity constraint qualifications and simplified \(B\)-stationary conditions for mathematical programs with equilibrium constraints
• Generalized differential calculus for nonsmooth and set-valued mappings
• Coderivatives in parametric optimization
• Weak via strong Stackelberg problem: New results
• Necessary optimality conditions for bilevel optimization problems using convexificators
• Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
• Ample Parameterization of Variational Inclusions
• Variational Analysis
• Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints
• Constraint Qualifications and Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints
• Nondifferentiable Multiplier Rules for Optimization and Bilevel Optimization Problems
• Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints
• Optimality conditions for bilevel programming problems