Characterizations of Approximate Duality and Saddle Point Theorems for Nonsmooth Robust Vector Optimization

2019 ◽  
Vol 41 (4) ◽  
pp. 462-482 ◽  
Author(s):  
Xiangkai Sun ◽  
Liping Tang ◽  
Jing Zeng
Keyword(s):  
Saddle Point ◽  
Vector Optimization ◽  
Approximate Duality

scholarly journals Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiaohong Hu ◽  
Zhimiao Fang ◽  
Yunxuan Xiong
Keyword(s):  
Saddle Point ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Efficient Solutions ◽  
Vector Optimization Problem ◽  
Well Posedness ◽  
Scalar Problem ◽  
New Type ◽  
Strict Efficiency ◽  
Multiplier Theorems

The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.

∊-STRICTLY EFFICIENT SOLUTIONS OF VECTOR OPTIMIZATION PROBLEMS WITH SET-VALUED MAPS

2007 ◽  
Vol 24 (06) ◽  
pp. 841-854 ◽  
Author(s):  
TAIYONG LI ◽  
YIHONG XU ◽  
CHUANXI ZHU
Keyword(s):  
Saddle Point ◽  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Lagrangian Multiplier ◽  
Multiplier Theorem ◽  
Lagrangian Multiplier Theorem

In this paper, the notion of ∊-strictly efficient solution for vector optimization with set-valued maps is introduced. Under the assumption of the ic-cone-convexlikeness for set-valued maps, the scalarization theorem, ∊-Lagrangian multiplier theorem, ∊-saddle point theorems and ∊-duality assertions are established for ∊-strictly efficient solution.

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