EXACT PENALIZATION AND NECESSARY OPTIMALITY CONDITIONS FOR GENERALIZED BILEVEL PROGRAMMING-PROBLEMS

The generalized bilevel programming problem (GBLP) is a bilevel mathem atical program where the lower level is a variational inequality. In t his paper we prove that if the objective function of a GBLP is uniform ly Lipschitz continuous in the lower level decision variable with resp ect to the upper level decision variable, then using certain uniform p arametric error bounds as penalty functions gives single level problem s equivalent to the GBLP. Several local and global uniform para metric error bounds are presented, and assumptions guaranteeing that they ap ply are discussed. We then derive Kuhn-Tucker-type necessary optimalit y conditions by using exact penalty formulations and nonsmooth analysi s.