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.

scholarly journals On duality for nonsmooth Lipschitz optimization problems

2009 ◽  
Vol 19 (1) ◽  
pp. 41-47 ◽  
Author(s):  
Vasile Preda ◽  
Miruna Beldiman ◽  
Antoan Bătătorescu
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Vector Optimization Problem ◽  
Duality Theorems ◽  
Lipschitz Optimization ◽  
Generalized Invexity

We present some duality theorems for a non-smooth Lipschitz vector optimization problem. Under generalized invexity assumptions on the functions the duality theorems do not require constraint qualifications.

scholarly journals Vector variational-like inequalities and vector optimization problems

2014 ◽  
Vol 30 (1) ◽  
pp. 101-108
Author(s):  
MIHAELA MIHOLCA ◽  
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Vector Optimization Problems ◽  
Limiting Subdifferential ◽  
Generalized Invexity ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Mordukhovich Limiting Subdifferential

In this paper, we present the concept of generalized invexity for vector-valued functions. Also, we consider different kinds of generalized vector variational-like inequality and a vector optimization problem. Some relations between vector variational-like inequalities and a vector optimization problem are established by using the properties of Mordukhovich limiting subdifferential.

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 Nondifferentiable G-Mond–Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1348 ◽  
Author(s):  
Ramu Dubey ◽  
Lakshmi Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Second Order ◽  
Type Model ◽  
Dual Model ◽  
Duality Theorems ◽  
Converse Duality ◽  
Numerical Example ◽  
Primal Dual

In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond–Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.

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