Constraint Qualifications and KKT Conditions for Bilevel Programming Problems
Mathematics of Operations Research
Necessary Optimality Conditions for Two-Stage Stochastic Programs with Equilibrium Constraints
SIAM Journal on Optimization
SIAM Journal on Optimization
SIAM Journal on Optimization
Necessary Optimality Conditions for Multiobjective Bilevel Programs
Mathematics of Operations Research
Mathematics of Operations Research
Weak Sharp Minima on Riemannian Manifolds
SIAM Journal on Optimization
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The generalized bilevel programming problem (GBLP) is a bilevel mathematical program where the lower level is a variational inequality. In this paper we prove that if the objective function of a GBLP is uniformly Lipschitz continuous in the lower level decision variable with respect to the upper level decision variable, then using certain uniform parametric error bounds as penalty functions gives single level problems equivalent to the GBLP. Several local and global uniform parametric error bounds are presented, and assumptions guaranteeing that they apply are discussed. We then derive Kuhn--Tucker-type necessary optimality conditions by using exact penalty formulations and nonsmooth analysis.