非光滑变分问题解的表征及对偶性

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Pub Date : 2013-09-06 DOI:10.5281/ZENODO.1088172

Juan Zhang, Changzhao Li

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引用次数: 0

摘要

本文在非光滑变分问题中引入了一类新的非光滑伪凸函数和非光滑拟凸函数。利用这些概念，建立了一类使用Clarke广义梯度的非光滑变分问题的若干充分必要条件。建立了弱、强、逆对偶关系。Keywords-Variational问题;非光滑pseudo-invex;非光滑quasi-invex;临界点;二元性

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Characterization of Solutions of Nonsmooth Variational Problems and Duality

In this paper, we introduce a new class of nonsmooth pseudo-invex and nonsmooth quasi-invex functions to non-smooth variational problems. By using these concepts, numbers of necessary and sufficient conditions are established for a nonsmooth variational problem wherein Clarke’s generalized gradient is used. Also, weak, strong and converse duality are established. Keywords—Variational problem; Nonsmooth pseudo-invex; Nonsmooth quasi-invex; Critical point; Duality

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来源期刊

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering

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