Existence of Solutions for Vector Optimization on Hadamard Manifolds

被引：0
作者：
Li-Wen Zhou
Nan-Jing Huang
机构：
[1] Sichuan University,Department of Mathematics
来源：
Journal of Optimization Theory and Applications | 2013年 / 157卷
关键词：
Hadamard manifold; Weak minimum; Vector optimization; Vector variational inequality; Geodesic convex;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a relationship between a vector variational inequality and a vector optimization problem is given on a Hadamard manifold. An existence of a weak minimum for a constrained vector optimization problem is established by an analogous to KKM lemma on a Hadamard manifold.
引用
收藏
页码：44 / 53
页数：9
相关论文
共 52 条
[1]  
Oveisiha M.(2012)Vector optimization problem and generalized convexity J. Glob. Optim. 52 29-43
[2]  
Zafarani J.(1983)On the existence of Pareto efficient points Math. Oper. Res. 8 64-73
[3]  
Borwein J.M.(1994)Existence and continuity of solutions for vector optimization J. Optim. Theory Appl. 81 459-467
[4]  
Chen G.Y.(1998)Characterizations of the nonemptiness and compactness of solution sets in convex vector optimization J. Optim. Theory Appl. 96 123-131
[5]  
Craven B.D.(1982)Existence and characterization of efficient decisions with respect to cones Math. Program. 23 111-116
[6]  
Deng S.(2006)Vector variational-like inequality and non-smooth vector optimization problems Nonlinear Anal. 64 1939-1945
[7]  
Henig M.I.(2009)Vector optimization and variational-like inequalities J. Glob. Optim. 43 47-66
[8]  
Mishraa S.K.(2004)Relationships between vector variational-like inequality and optimization problems Eur. J. Oper. Res. 157 113-119
[9]  
Wang S.Y.(1991)Geodesic convexity in nonlinear optimization J. Optim. Theory Appl. 69 169-183
[10]  
Rezaie M.(2005)Singularities of monotone vector fields and an extragradient-type algorithm J. Glob. Optim. 31 133-151
123456