Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces
Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces
复制标题
DOI：
10.1007/s10957-012-0045-2
复制
发表时间：
2012-04
影响因子：
1.9
通讯作者：
Zhiang Zhou;Jian-Wen Peng
中科院分区：
文献类型：
--
作者：
Zhiang Zhou;Jian-Wen Peng
在实序线性空间中，首次建立了集值映射广义锥次似凸性的等价刻画。其次，在集值映射的广义锥次似凸性假设下，得到了集值优化问题在ϵ弱有效性意义下的标量化定理。最后，通过标量化的方法，得到了集值优化问题的ϵ全局真有效元的存在性定理。本文的结果推广和改进了文献中的一些已知结果。
In real ordered linear spaces, an equivalent characterization of generalized cone subconvexlikeness of set-valued maps is firstly established. Secondly, under the assumption of generalized cone subconvexlikeness of set-valued maps, a scalarization theorem of set-valued optimization problems in the sense ofϵ-weak efficiency is obtained. Finally, by a scalarization approach, an existence theorem ofϵ-global properly efficient element of set-valued optimization problems is obtained. The results in this paper generalize and improve some known results in the literature.