Proper efficiency conditions and duality results for nonsmooth vector optimization in Banach spaces under -invexity

2012 ◽  
Vol 75 (6) ◽  
pp. 3107-3121 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Proper Efficiency ◽  
Duality Results ◽  
Nonsmooth Vector Optimization ◽  
Optimization In Banach Spaces ◽  
Efficiency Conditions

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 A class of semilocal E-preinvex maps in Banach spaces with applications to nondifferentiable vector optimization

2013 ◽  
Vol 4 (1) ◽  
pp. 1-10
Author(s):  
Hehua Jiao
Keyword(s):  
Optimality Conditions ◽  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Basic Properties ◽  
New Class ◽  
Duality Results

In this paper, a new class of semilocal E-preinvex and related maps in Banach spaces is introduced for a nondifferentiable vector optimization problem with restrictions of inequalities and some of its basic properties are studied. Furthermore, as its applications, some optimality conditions and duality results are established for a nondifferentiable vector optimization under the aforesaid maps assumptions.

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