Constraint Qualifications and KKT Conditions for Bilevel Programming Problems

Authors:
Jane J. Ye
Affiliations:
Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3P4
Venue:
Mathematics of Operations Research
Year:
2006

Citing 11
Cited 3

Convexity and concavity properties of the optimal value function in parametric nonlinear programming

Journal of Optimization Theory and Applications
Necessary optimality conditions for Stackelberg problems

Journal of Optimization Theory and Applications
Constraint qualifications and Lagrange multipliers in nondifferentiable programming problems

Journal of Optimization Theory and Applications
Complementarity Constraint Qualifications and Simplified B-Stationarity Conditions for Mathematical Programs with Equilibrium Constraints

Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity

Mathematics of Operations Research
Sensitivity Analysis of the Value Function for Optimization Problems with Variational Inequality Constraints

SIAM Journal on Control and Optimization
Constraint Qualifications and Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints

SIAM Journal on Optimization
Exact Penalization and Necessary Optimality Conditions for Generalized Bilevel Programming Problems

SIAM Journal on Optimization
Erratum: Sensitivity Analysis of the Value Function for Optimization Problems With Variational Inequality Constraints

SIAM Journal on Control and Optimization
Nondifferentiable Multiplier Rules for Optimization and Bilevel Optimization Problems

SIAM Journal on Optimization
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)

Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)

Global solution of nonlinear mixed-integer bilevel programs

Journal of Global Optimization
New Necessary Optimality Conditions for Bilevel Programs by Combining the MPEC and Value Function Approaches

SIAM Journal on Optimization
Necessary Optimality Conditions for Multiobjective Bilevel Programs

Mathematics of Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we consider the bilevel programming problem (BLPP), which 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. We extend well-known constraint qualifications for nonlinear programming problems such as the Abadie constraint qualification, the Kuhn-Tucker constraint qualification, the Zangwill constraint qualification, the Arrow-Hurwicz-Uzawa constraint qualification, and the weak reverse convex constraint qualification to BLPPs and derive a Karash-Kuhn-Tucker (KKT)-type necessary optimality condition under these constraint qualifications without assuming the lower-level problem satisfying the Mangasarian Fromovitz constraint qualification. Relationships among various constraint qualifications are also given.