scholarly journals Local Sharp Vector Variational Type Inequality and Optimization Problems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1844
Author(s):  
Jong Kyu Kim ◽  
Salahuddin
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Type Inequality ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Lipschitzian Functions ◽  
Locally Lipschitzian Functions ◽  
The Relationship ◽  
Variational Type ◽  
Convexity Conditions

In this paper, our goal was to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate η-convexity conditions for locally Lipschitzian functions.

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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