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数学进展 - 2016, Vol. 45(2): 289-298
研究论文
巴拿赫空间中广义I型一致不变凸条件下带锥约束的向量优化问题
Vector Optimization With Cone Constraints Under Generalized Type I Univexity in Banach Spaces

焦合华1,刘三阳2
JIAO Hehua1, LIU Sanyang2

1. 长江师范学院数学与统计学院, 重庆, 408100;
2. 西安电子科技大学数学与统计学院, 西安, 陕西, 710071
1. School of Mathematics and Statistics,Yangtze Normal University, Chongqing, 408100, P. R. China;
2. School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi, 710071, P. R. China

收稿日期: 2014-07-24
出版日期: 2016-03-10
2016, Vol. 45(2): 289-298
DOI: 10.11845/sxjz.2014114b


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摘要 本文在巴拿赫空间中为一类带锥约束的向量优化问题引入了一些$\alpha$-d I型一致不变凸函数的新概念.建立了一些 Karush-Kuhn-Tucker型最优性充分条件.而且建立了一个Mond-Weir型对偶, 在各种$\alpha$-d I型一致不变凸性条件下得到了弱对偶、强对偶和逆对偶定理.
Abstract:In this paper, we introduce new concepts of $\alpha$-d-type I univex functions between Banach spaces for a vector optimization problem with cone constraints. We establish some Karush-Kuhn-Tucker type sufficient optimality conditions for a feasible point to be a weakly efficient (or an efficient) solution. Moreover, a Mond-Weir type dual is formulated and weak, strong and converse duality results are obtained under various types of $\alpha$-d-type I univexity assumptions.
PACS:  O221.6  
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