scholarly journals On the Generic Uniqueness of Pareto-Efficient Solutions of Vector Optimization Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Dejin Zhang ◽  
Shuwen Xiang ◽  
Yanlong Yang ◽  
Xicai Deng
Keyword(s):  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Baire Category ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Weakly Efficient Solution ◽  
Weakly Efficient Solutions ◽  
Pareto Efficient ◽  
Generic Uniqueness

In this paper, the generic uniqueness of Pareto weakly efficient solutions, especially Pareto-efficient solutions, of vector optimization problems is studied by using the nonlinear and linear scalarization methods, and some further results on the generic uniqueness are proved. These results present that, for most of the vector optimization problems in the sense of the Baire category, the Pareto weakly efficient solution, especially the Pareto-efficient solution, is unique. Furthermore, based on these results, the generic Tykhonov well-posedness of vector optimization problems is given.

Lagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued maps

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Renying Zeng
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Lagrangian Multipliers ◽  
Weakly Efficient Solutions ◽  
Affine Maps ◽  
Convex Vector Optimization ◽  
Affine Set

Abstract In this paper, we introduce some definitions of generalized affine set-valued maps: affinelike, preaffinelike, nearaffinelike, and prenearaffinelike maps. We present examples to explain that our definitions of generalized affine maps are different from each other. We derive a theorem of alternative of Farkas–Minkowski type, discuss Lagrangian multipliers for constrained set-valued optimization problems, and obtain some optimality conditions for weakly efficient solutions.

∊-STRICTLY EFFICIENT SOLUTIONS OF VECTOR OPTIMIZATION PROBLEMS WITH SET-VALUED MAPS

2007 ◽  
Vol 24 (06) ◽  
pp. 841-854 ◽  
Author(s):  
TAIYONG LI ◽  
YIHONG XU ◽  
CHUANXI ZHU
Keyword(s):  
Saddle Point ◽  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Lagrangian Multiplier ◽  
Multiplier Theorem ◽  
Lagrangian Multiplier Theorem

In this paper, the notion of ∊-strictly efficient solution for vector optimization with set-valued maps is introduced. Under the assumption of the ic-cone-convexlikeness for set-valued maps, the scalarization theorem, ∊-Lagrangian multiplier theorem, ∊-saddle point theorems and ∊-duality assertions are established for ∊-strictly efficient solution.

scholarly journals A note of stability of weakly efficient solution set for optimization with set-valued maps

2003 ◽  
Vol 16 (3) ◽  
pp. 267-273
Author(s):  
Luo Qun
Keyword(s):  
Efficient Solution ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Baire Category ◽  
Efficient Solutions ◽  
Solution Set ◽  
Weakly Efficient Solution ◽  
Solution Sets ◽  
Essential Components ◽  
Efficient Solution Set

In this paper, we study the stability of weakly efficient solution sets for optimization problems with set-valued maps. We introduce the concept of essential weakly efficient solutions and essential components of weakly efficient solution sets. We first show that most optimization problems with set-valued maps (in the sense of Baire category) are stable. Secondly, we obtain some sufficient conditions for the existence of one essential weakly efficient solution or one essential component of the weakly efficient solution set .

On Second-Order Composed Proto-Differentiability of Proper Perturbation Maps in Parametric Vector Optimization Problems

2020 ◽  
pp. 2050040
Author(s):  
Le Thanh Tung
Keyword(s):  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Second Order ◽  
Vector Optimization Problems ◽  
Solution Maps ◽  
Qualification Conditions ◽  
Parametric Vector Optimization ◽  
Perturbation Maps ◽  
Proper Efficient Solution

The main aim of this paper is to study second-order sensitivity analysis in parametric vector optimization problems. We prove that the proper perturbation maps and the proper efficient solution maps of parametric vector optimization problems are second-order composed proto-differentiable under some appropriate qualification conditions. Some examples are provided to illustrate our results.

Sign in / Sign up

Export Citation Format

Share Document