New Sequential Lagrange Multiplier Conditions Characterizing Optimality without Constraint Qualification for Convex Programs
New Sequential Lagrange Multiplier Conditions Characterizing Optimality without Constraint Qualification for Convex Programs
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DOI：
10.1137/s1052623402417699
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
V. Jeyakumar;G. M. Lee;N. Dinh
中科院分区：
文献类型：
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作者：
V. Jeyakumar;G. M. Lee;N. Dinh
在本文中，根据子差异和$ \ epsilon $ -subdifferentials，介绍了一个新的顺序Lagrange乘数表征最优性，而没有限制的最佳资格。还得出了仅涉及亚差异的顺序条件，但在附近的约束点最小化的点也被得出了。对于平滑的凸面程序，顺序条件在附近点产生了限制的库恩 - 塔克条件，而没有约束资格。它显示了顺序条件与标准Lagrange乘数条件的关系。给出了半决赛程序，半侵犯程序和半五号程序的应用程序。讨论了几个数值示例，以说明顺序条件的重要性。
In this paper a new sequential Lagrange multiplier condition characterizing optimality without a constraint qualification for an abstract nonsmooth convex program is presented in terms of the subdifferentials and the $\epsilon$-subdifferentials. A sequential condition involving only the subdifferentials, but at nearby points to the minimizer for constraints, is also derived. For a smooth convex program, the sequential condition yields a limiting Kuhn--Tucker condition at nearby points without a constraint qualification. It is shown how the sequential conditions are related to the standard Lagrange multiplier condition. Applications to semidefinite programs, semi-infinite programs, and semiconvex programs are given. Several numerical examples are discussed to illustrate the significance of the sequential conditions.