scholarly journals Vector Critical Points and Cone Efficiency in Nonsmooth Vector Optimization

2020 ◽  
Author(s):  
Tadeusz Antczak ◽  
Marcin Studniarski
Keyword(s):  
Vector Optimization ◽  
Critical Points ◽  
Nonsmooth Vector Optimization

Critical Points Index for Vector Functions and Vector Optimization

2008 ◽  
Vol 138 (3) ◽  
pp. 479-496 ◽  
Author(s):  
E. Miglierina ◽  
E. Molho ◽  
M. Rocca
Keyword(s):  
Vector Optimization ◽  
Critical Points

Vector critical points and efficiency in vector optimization with Lipschitz functions

2015 ◽  
Vol 10 (1) ◽  
pp. 47-62 ◽  
Author(s):  
C. Gutiérrez ◽  
B. Jiménez ◽  
V. Novo ◽  
G. Ruiz-Garzón
Keyword(s):  
Vector Optimization ◽  
Critical Points ◽  
Lipschitz Functions

scholarly journals G-α-preinvex functions and non-smooth vector optimization problems

2021 ◽  
pp. 8-8
Author(s):  
Yu Chen
Keyword(s):  
Vector Optimization ◽  
Critical Points ◽  
Optimization Problems ◽  
Efficient Points ◽  
Vector Optimization Problems ◽  
Solution Properties ◽  
Smooth Vector ◽  
Inequality Problem ◽  
Preinvex Functions ◽  
Weak Vector

In this paper, we proposed the non-smooth G-?-preinvexity by generalizing ?-invexity and G-preinvexity, and discussed some solution properties about non-smooth vector optimization problems and vector variational-like inequality problems under the condition of non-smooth G-?-preinvexity. Moreover, we also proved that the vector critical points, the weakly efficient points and the solutions of the non-smooth weak vector variational-like inequality problem are equivalent under non-smooth pseudo-G-?-preinvexity assumptions.

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.

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