scholarly journals Optimality conditions for $ E $-differentiable vector optimization problems with the multiple interval-valued objective function

2020 ◽  
Vol 16 (6) ◽  
pp. 2971-2989
Author(s):  
Tadeusz Antczak ◽  
◽  
Najeeb Abdulaleem ◽  
Keyword(s):  
Objective Function ◽  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Differentiable Vector ◽  
Interval Valued

scholarly journals E-invexity and generalized E-invexity in E-differentiable multiobjective programming

2019 ◽  
Vol 24 ◽  
pp. 01002 ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Differentiable Function ◽  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Vector Optimization Problems ◽  
Invex Functions ◽  
Differentiable Vector

In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E-differentiable function, the concept of E-invexity is introduced as a generalization of the E-differentiable E-convexity notion. In addition, some properties of E-differentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problems with both inequality and equality constraints. Also, the sufficiency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-differentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex.

Sign in / Sign up

Export Citation Format

Share Document