scholarly journals Saddle point criteria for second order $\eta$-approximated vector optimization problems

Kybernetika ◽  
2016 ◽  
pp. 359-378 ◽  
Author(s):  
Anurag Jayswal ◽  
Shalini Jha ◽  
Sarita Choudhury
Keyword(s):  
Saddle Point ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Vector Optimization Problems

On Second-Order Composed Proto-Differentiability of Proper Perturbation Maps in Parametric Vector Optimization Problems

2020 ◽  
pp. 2050040
Author(s):  
Le Thanh Tung
Keyword(s):  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Second Order ◽  
Vector Optimization Problems ◽  
Solution Maps ◽  
Qualification Conditions ◽  
Parametric Vector Optimization ◽  
Perturbation Maps ◽  
Proper Efficient Solution

The main aim of this paper is to study second-order sensitivity analysis in parametric vector optimization problems. We prove that the proper perturbation maps and the proper efficient solution maps of parametric vector optimization problems are second-order composed proto-differentiable under some appropriate qualification conditions. Some examples are provided to illustrate our results.

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.

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