scholarly journals The Optimality Conditions of Differentiable Vector Optimization Problems

1996 ◽  
Vol 201 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Li Zemin
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Differentiable Vector

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.

scholarly journals Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

2017 ◽  
Vol 9 (4) ◽  
pp. 168
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Scalar Optimization ◽  
Scalar And Vector Optimization

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

scholarly journals Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Duality Theorems ◽  
Differentiable Vector

AbstractIn this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

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