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.

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 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 Vector optimization with cone semilocally preinvex functions

2013 ◽  
Vol 4 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Surjeet Kaur Suneja ◽  
Meetu Bhatia
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Minimization Problem ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Preinvex Functions ◽  
Necessary And Sufficient

In this paper we introduce cone semilocally preinvex, cone semilocally quasi preinvex and cone semilocally pseudo preinvex functions and study their properties. These functions are further used to establish necessary and sufficient optimality conditions for a vector minimization problem over cones. A Mond-Weir type dual is formulated for the vector optimization problem and various duality theorems are proved.

Efficiency and duality for vector optimization problem on Riemannian manifolds involving KT-B-invexity

2019 ◽  
Vol 12 (07) ◽  
pp. 1950088
Author(s):  
Babli Kumari ◽  
Anurag Jayswal
Keyword(s):  
Vector Optimization ◽  
Riemannian Manifolds ◽  
Efficient Solution ◽  
Optimization Problem ◽  
Dual Problem ◽  
Vector Optimization Problem ◽  
Converse Duality ◽  
Duality Results ◽  
Weak Efficient Solution

In this paper, we consider a vector optimization problem on Riemannian manifolds for which we define KT-B-invex and KT-B-pseudoinvex functions. Further, we prove that every vector Kuhn–Tucker point is a weak efficient solution for considered vector optimization problem under the suitable assumptions. Moreover, we also study the Mond–Weir dual problem for the aforesaid problem and establish its weak, strong and converse duality results.

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.

Optimality and duality for vector optimization problem with non-convex feasible set

OPSEARCH ◽  
2019 ◽  
Vol 57 (1) ◽  
pp. 1-12 ◽  
Author(s):  
S. K. Suneja ◽  
Sunila Sharma ◽  
Priyanka Yadav
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Feasible Set ◽  
Optimality And Duality

scholarly journals Vector variational inequalities and their relations with vector optimization

2013 ◽  
Vol 4 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Surjeet Kaur Suneja ◽  
Bhawna Kohli
Keyword(s):  
Variational Inequalities ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Clarke Subdifferential ◽  
Vector Variational Inequalities ◽  
Regularity Assumption ◽  
Weak Minimum ◽  
Minimum Solution ◽  
Clarke Subdifferentials

In this paper, K- quasiconvex, K- pseudoconvex and other related functions have been introduced in terms of their Clarke subdifferentials, where   is an arbitrary closed convex, pointed cone with nonempty interior. The (strict, weakly) -pseudomonotonicity, (strict) K- naturally quasimonotonicity and K- quasimonotonicity of Clarke subdifferential maps have also been defined. Further, we introduce Minty weak (MVVIP) and Stampacchia weak (SVVIP) vector variational inequalities over arbitrary cones. Under regularity assumption, we have proved that a weak minimum solution of vector optimization problem (VOP) is a solution of (SVVIP) and under the condition of K- pseudoconvexity we have obtained the converse for MVVIP (SVVIP). In the end we study the interrelations between these with the help of strict K-naturally quasimonotonicity of Clarke subdifferential map.

Derivatives of Hadamard type in vector optimization

2018 ◽  
Vol 68 (2) ◽  
pp. 421-430
Author(s):  
Karel Pastor
Keyword(s):  
Nonlinear Analysis ◽  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimality Condition ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Dini Derivatives ◽  
Scalar Optimality ◽  
Derivatives Of

Abstract In our paper we will continue the comparison which was started by Vsevolod I. Ivanov [Nonlinear Analysis 125 (2015), 270–289], where he compared scalar optimality conditions stated in terms of Hadamard derivatives for arbitrary functions and those which was stated for ℓ-stable functions in terms of Dini derivatives. We will study the vector optimization problem and we show that also in this case the optimality condition stated in terms of Hadamard derivatives is more advantageous.

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