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Volume 24, Issue 6
On Karush-Kuhn-Tucker Points for a Smoothing Method in Semi-Infinite Optimization

Oliver Stein

J. Comp. Math., 24 (2006), pp. 719-732.

Published online: 2006-12

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  • Abstract

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.  

  • Keywords

Generalized semi-infinite optimization, Stackelberg game, Constraint qualification, Smoothing, NCP function.

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-719, author = {Oliver Stein}, title = {On Karush-Kuhn-Tucker Points for a Smoothing Method in Semi-Infinite Optimization}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {6}, pages = {719--732}, abstract = {

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.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8786.html} }
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 -

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.  

Oliver Stein. (2006). On Karush-Kuhn-Tucker Points for a Smoothing Method in Semi-Infinite Optimization. Journal of Computational Mathematics. 24 (6). 719-732. doi:
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