On Karush-kuhn-tucker Points for a Smoothing Method in Semi-infinite Optimization *1)

We study the smoothing method for the solution of generalized semi-infinite optimization problems from (O. Stein, G. Still: Solving semi-infinite optimization problems with interior point techniques, SIAM J. Control Optim., 42(2003), pp. 769–788). It is shown that Karush-Kuhn-Tucker points of the smoothed problems do not necessarily converge to a Karush-Kuhn-Tucker point of the original problem, as could be expected from results in (F. Facchinei, H. Jiang, L. Qi: A smoothing method for mathematical programs with equilibrium constraints, Math. Program., 85(1999), pp. 107–134). Instead, they might merely converge to a Fritz John point. We give, however, different additional assumptions which guarantee convergence to Karush-Kuhn-Tucker points. Mathematics subject classification: 90C34, 90C25, 49M37, 65K05.