鞍点
矢量优化
数学
马鞍
数学优化
最优化问题
功能(生物学)
有序向量空间
班级(哲学)
分离(统计)
向量空间
点(几何)
矢量场
应用数学
计算机科学
纯数学
人工智能
生物化学
化学
几何学
统计
功能分析
进化生物学
基因
插值空间
生物
多群优化
作者
Jiawei Chen,Shengjie Li,Jen‐Chih Yao
出处
期刊:Journal of Industrial and Management Optimization
[American Institute of Mathematical Sciences]
日期:2019-01-03
卷期号:16 (2): 707-724
被引量:3
摘要
In this paper, we consider a class of constrained vector optimization problems by using image space analysis. A class of vector-valued separation functions and a $ \mathfrak{C} $-solution notion are proposed for the constrained vector optimization problems, respectively. Moreover, existence of a saddle point for the vector-valued separation function is characterized by the (regular) separation of two suitable subsets of the image space. By employing the separation function, we introduce a class of generalized vector-valued Lagrangian functions without involving any elements of the feasible set of constrained vector optimization problems. The relationships between the type-Ⅰ(Ⅱ) saddle points of the generalized Lagrangian functions and that of the function corresponding to the separation function are also established. Finally, optimality conditions for $ \mathfrak{C} $-solutions of constrained vector optimization problems are derived by the saddle-point conditions.
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