Criticality of Lagrange Multipliers in Variational Systems
Criticality of Lagrange Multipliers in Variational Systems
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DOI：
10.1137/18m1206862
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
B. Mordukhovich;Ebrahim Sarabi
中科院分区：
文献类型：
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作者：
B. Mordukhovich;Ebrahim Sarabi
本文研究变分系统中的拉格朗日乘子的临界性，它在最优化和变分分析的理论和数值方面都得到了公认。与以前的发展与多面体KKT系统等，我们现在专注于一般的非多面体系统，特别是与圆锥规划的问题。开发一种新的方法，这主要是基于先进的技术和工具的二阶变分分析和广义微分，使我们能够克服主要的挑战，非多面体，并建立完整的非临界乘数在这样的设置。所得结果通过半定规划的例子加以说明。
The paper concerns the study of criticality of Lagrange multipliers in variational systems that has been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments dealing with polyhedral KKT systems and the like, we now focus on general nonpolyhedral systems that are associated, in particular, with problems of conic programming. Developing a novel approach, which is mainly based on advanced techniques and tools of second-order variational analysis and generalized differentiation, allows us to overcome principal challenges of nonpolyhedrality and to establish complete characterizations on noncritical multipliers in such settings. The obtained results are illustrated by examples from semidefinite programming.