scholarly journals On essential sets and essential components of efficient solutions for vector optimization problems

2006 ◽  
Vol 315 (1) ◽  
pp. 317-326 ◽  
Author(s):  
Shuwen Xiang ◽  
Yonghui Zhou
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Essential Components ◽  
Essential Sets

Lagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued maps

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Renying Zeng
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Lagrangian Multipliers ◽  
Weakly Efficient Solutions ◽  
Affine Maps ◽  
Convex Vector Optimization ◽  
Affine Set

Abstract In this paper, we introduce some definitions of generalized affine set-valued maps: affinelike, preaffinelike, nearaffinelike, and prenearaffinelike maps. We present examples to explain that our definitions of generalized affine maps are different from each other. We derive a theorem of alternative of Farkas–Minkowski type, discuss Lagrangian multipliers for constrained set-valued optimization problems, and obtain some optimality conditions for weakly efficient solutions.

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