Nonlinear separation in the image space with applications to penalty methods
Nonlinear separation in the image space with applications to penalty methods
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DOI：
10.1080/00036811.2011.614603
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发表时间：
2012-09
影响因子：
1.1
通讯作者：
G. Mastroeni
中科院分区：
文献类型：
--
作者：
G. Mastroeni
在这篇文章中，我们分析了一个非线性分离方案在图像空间与一个无限维锥约束极值问题，特别是，我们考虑的应用，非线性拉格朗日对偶和精确和不精确的外部惩罚方法。对偶和精确罚方法产生于正则非线性分离的存在性，这被证明是等价于与给定问题相关的广义拉格朗日函数的鞍点条件，而不精确罚方法与渐近非线性分离的存在性密切相关。
In this article we analyse a nonlinear separation scheme in the image space associated with an infinite-dimensional cone constrained extremum problem, and, in particular, we consider the applications to nonlinear Lagrangian duality and exact and inexact exterior penalty methods. Duality and exact penalty methods arise from the existence of a regular nonlinear separation, which is shown to be equivalent to a saddle point condition for a generalized Lagrangian function associated with the given problem, while inexact penalty methods are closely related with the existence of an asymptotic nonlinear separation.