scholarly journals Strict Benson proper-ε-efficiency in vector optimization with set-valued maps

2015 ◽  
Vol 25 (3) ◽  
pp. 387-395
Author(s):  
Kaur Suneja ◽  
Megha Sharma_
Keyword(s):  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Lagrangian Multiplier ◽  
Multiplier Theorems ◽  
Proper Efficient Solution

In this paper the notion of Strict Benson proper-?-efficient solution for a vector optimization problem with set-valued maps is introduced. The scalarization theorems and ?-Lagrangian multiplier theorems are established under the assumption of ic-cone-convexlikeness of set-valued maps.

scholarly journals Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiaohong Hu ◽  
Zhimiao Fang ◽  
Yunxuan Xiong
Keyword(s):  
Saddle Point ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Efficient Solutions ◽  
Vector Optimization Problem ◽  
Well Posedness ◽  
Scalar Problem ◽  
New Type ◽  
Strict Efficiency ◽  
Multiplier Theorems

The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.

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 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.

scholarly journals Duality Theorem for a Minimax Vector Optimization Problem

2021 ◽  
Author(s):  
Jacob Atticus Armstrong Goodall
Keyword(s):  
Vector Optimization ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Optimal Transport ◽  
Probability Distributions ◽  
Vector Optimization Problem ◽  
Complexity Science ◽  
Polish Spaces ◽  
Leibler Divergence ◽  
Mathematical Optimisation

Abstract A duality theorem is stated and proved for a minimax vector optimization problem where the vectors are elements of the set of products of compact Polish spaces. A special case of this theorem is derived to show that two metrics on the space of probability distributions on countable products of Polish spaces are identical. The appendix includes a proof that, under the appropriate conditions, the function studied in the optimisation problem is indeed a metric. The optimisation problem is comparable to multi-commodity optimal transport where there is dependence between commodities. This paper builds on the work of R.S. MacKay who introduced the metrics in the context of complexity science in [4] and [5]. The metrics have the advantage of measuring distance uniformly over the whole network while other metrics on probability distributions fail to do so (e.g total variation, Kullback–Leibler divergence, see [5]). This opens up the potential of mathematical optimisation in the setting of complexity science.

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.

Sign in / Sign up

Export Citation Format

Share Document