TY - JOUR
T1 - On Karush-Kuhn-Tucker Points for a Smoothing Method in Semi-Infinite Optimization
AU - Oliver Stein
JO - Journal of Computational Mathematics
VL - 6
SP - 719
EP - 732
PY - 2006
DA - 2006/12
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8786.html
KW - Generalized semi-infinite optimization, Stackelberg game, Constraint qualification, Smoothing, NCP function.
AB - <p style="text-align: justify;">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. &nbsp;</p>