Higher Order Efficiency, Saddle Point Optimality, and Duality for Vector Optimization Problems

2007 ◽  
Vol 28 (3-4) ◽  
pp. 339-352 ◽  
Author(s):  
Anjana Gupta ◽  
Davinder Bhatia ◽  
Aparna Mehra
Keyword(s):  
Saddle Point ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Higher Order ◽  
Vector Optimization Problems ◽  
Optimality And Duality

∊-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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