First and second order optimality conditions in vector optimization problems with nontransitive preference relation

2016 ◽  
Vol 292 (S1) ◽  
pp. 91-105
Author(s):  
V. V. Gorokhovik ◽  
M. A. Trafimovich
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Preference Relation ◽  
Second Order ◽  
Vector Optimization Problems ◽  
Second Order Optimality Conditions

scholarly journals On generalized derivatives forC1,1vector optimization problems

2003 ◽  
Vol 2003 (7) ◽  
pp. 365-376 ◽  
Author(s):  
Davide La Torre
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Vector Optimization Problems ◽  
Directional Derivatives ◽  
Generalized Derivatives ◽  
Second Order Optimality Conditions

We introduce generalized definitions of Peano and Riemann directional derivatives in order to obtain second-order optimality conditions for vector optimization problems involvingC1,1data. We show that these conditions are stronger than those in literature obtained by means of second-order Clarke subdifferential.

A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems

2018 ◽  
Vol 52 (2) ◽  
pp. 567-575 ◽  
Author(s):  
Do Sang Kim ◽  
Nguyen Van Tuyen
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Second Order ◽  
Vector Optimization Problems ◽  
Smooth Vector ◽  
Incorrect Result

The aim of this note is to present some second-order Karush–Kuhn–Tucker necessary optimality conditions for vector optimization problems, which modify the incorrect result in ((10), Thm. 3.2).

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