Erratum to: New Constraint Qualifications and Optimality Conditions for Second Order Cone Programs

2021 ◽  
Author(s):  
R. Andreani ◽  
E. H. Fukuda ◽  
G. Haeser ◽  
H. Ramírez ◽  
D. O. Santos ◽  
...  
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualifications ◽  
Second Order ◽  
Second Order Cone

scholarly journals Nonsmooth Vector Optimization Problem Involving Second-Order Semipseudo, Semiquasi Cone-Convex Functions

2020 ◽  
Vol 9 (2) ◽  
pp. 383-398
Author(s):  
Sunila Sharma ◽  
Priyanka Yadav
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Convex Functions ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Duality Results ◽  
Nonsmooth Vector Optimization ◽  
Second Order Cone

Recently, Suneja et al. [26] introduced new classes of second-order cone-(η; ξ)-convex functions along with theirgeneralizations and used them to prove second-order Karush–Kuhn–Tucker (KKT) type optimality conditions and duality results for the vector optimization problem involving first-order differentiable and second-order directionally differentiable functions. In this paper, we move one step ahead and study a nonsmooth vector optimization problem wherein the functions involved are first and second-order directionally differentiable. We introduce new classes of nonsmooth second-order cone-semipseudoconvex and nonsmooth second-order cone-semiquasiconvex functions in terms of second-order directional derivatives. Second-order KKT type sufficient optimality conditions and duality results for the same problem are proved using these functions.

scholarly journals Notes on Constraint Qualifications for Second-Order Optimality Conditions

2019 ◽  
Vol 11 (5) ◽  
pp. 16
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Second Order ◽  
Necessary Optimality Condition ◽  
First Order ◽  
Second Order Optimality Conditions ◽  
Order Constraint ◽  
Local Approximations ◽  
Abadie Constraint Qualification

In the first part of this paper we point out some basic properties of the critical cones used in second-order optimality conditions and give a simple proof of a strong second-order necessary optimality condition by assuming a “modified” first-order Abadie constraint qualification. In the second part we give some insights on second-order constraint qualifications related to second-order local approximations of the feasible set.

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