复合优化问题的Fenchel对偶

方东辉

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (2) : 528-536.

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系统科学与数学 ›› 2017, Vol. 37 ›› Issue (2) : 528-536. DOI: 10.12341/jssms13081
论文

复合优化问题的Fenchel对偶

    方东辉
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Study on the Fenchel Dualities for Composite Optimization Problems

    FANG Donghui
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摘要

利用共轭函数的上图性质, 引入新的约束规范条件, 建立了复合优化问题与其对偶问题之间的强对偶, 稳定强对偶及稳定全对偶成立的等价刻画,推广了前人的相关结论.

Abstract

By using the epigraph technique, we give some new constraint qualifications, which completely characterize the strong duality, the total duality, the stable strong duality and the stable total duality between the primal problem with its dual problem. The results of the present paper extend the corresponding ones in the previous paper.

关键词

复合优化问题 / 约束规范条件 / 强对偶 / 全对偶.

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方东辉. 复合优化问题的Fenchel对偶. 系统科学与数学, 2017, 37(2): 528-536. https://doi.org/10.12341/jssms13081
FANG Donghui. Study on the Fenchel Dualities for Composite Optimization Problems. Journal of Systems Science and Mathematical Sciences, 2017, 37(2): 528-536 https://doi.org/10.12341/jssms13081
中图分类号: 90C26    90C46   
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