On Connectedness of Efficient Solution Sets for a Star Cone-Quasiconvex Vector Optimization Problem

2007 ◽  
Vol 23 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Wen Song ◽  
Bo-ying Wu ◽  
Jian-mei Zhang
2015 ◽  
Vol 25 (3) ◽  
pp. 387-395
Author(s):  
Kaur Suneja ◽  
Megha Sharma_

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.


2019 ◽  
Vol 12 (07) ◽  
pp. 1950088
Author(s):  
Babli Kumari ◽  
Anurag Jayswal

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.


Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 947
Author(s):  
Xin Xu ◽  
Yang Dong Xu

The connectedness and path connectedness of the solution sets to vector optimization problems is an important and interesting study in optimization theories and applications. Most papers involving the direction established the connectedness and connectedness for the solution sets of vector optimization problems or vector equilibrium problems by means of the linear scalarization method rather than the nonlinear scalarization method. The aim of the paper is to deal with the connectedness and the path connectedness for the weak efficient solution set to a vector optimization problem by using the nonlinear scalarization method. Firstly, the union relationship between the weak efficient solution set to the vector optimization problem and the solution sets to a series of parametric scalar minimization problems, is established. Then, some properties of the solution sets of scalar minimization problems are investigated. Finally, by using the union relationship, the connectedness and the path connectedness for the weak efficient solution set of the vector optimization problem are obtained.


Author(s):  
Surjeet Kaur Suneja ◽  
Bhawna Kohli

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.


2018 ◽  
Vol 68 (2) ◽  
pp. 421-430
Author(s):  
Karel Pastor

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.


2021 ◽  
Author(s):  
Jacob Atticus Armstrong Goodall

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.


2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Najeeb Abdulaleem

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