Painlevé–Kuratowski stability of approximate efficient solutions for perturbed semi-infinite vector optimization problems

2017 ◽  
Vol 12 (6) ◽  
pp. 1339-1356 ◽  
Author(s):  
Z. Y. Peng ◽  
X. B. Li ◽  
X. J. Long ◽  
X. D. Fan
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Approximate Efficient Solutions

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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