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首页> 外文会议>The 8th international conference on optimization: Techniques and Applications >Exact Regularization of Nonlinear Programs and Applications
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Exact Regularization of Nonlinear Programs and Applications

机译：非线性程序的精确正则化及其应用

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The regularization of a nonlinear program is exact if all solutions of the regularized problem are also solutions of the original problem for all values of the regularization parameter below some positive threshold. In this talk, we show that the regularization is exact if and only if the Lagrangian function of a certain selection problem has a saddle point. Moreover, the regularization parameter threshold is inversely related to the Lagrange multiplier associated with the saddle point. Our results not only provide a fresh perspective on exact regularization but also extend the main results of Friedlander and Tseng [2] on a characterization of exact regularization of a convex program to that of a nonlinear (not necessarily convex) program. We also examine inner-connections among exact regularization, exact penalization of nonlinear programs and the existence of a weak sharp minimum for certain associated nonlinear programs.
机译：如果正则化问题的所有解也都是正则化参数低于某个正阈值的所有值的原始问题的解，则非线性程序的正则化是精确的。在本文中，我们证明正则化是正确的，当且仅当某个选择问题的拉格朗日函数具有一个鞍点时。此外，正则化参数阈值与与鞍点关联的拉格朗日乘数成反比。我们的结果不仅为精确正则化提供了新的视角，而且还将Friedlander和Tseng [2]在凸程序的精确正则化表征上的主要结果扩展为非线性（不一定是凸）程序的主要结果。我们还研究了非线性程序的精确正则化，精确罚分以及某些关联的非线性程序的弱尖锐最小值之间的内在联系。

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