Stability for the Major Joint Cone Weakly Efficient Solution Sets of Group Multiobjective Programming in Banach Space

2014 ◽  
Author(s):  
Xuanwei Zhou
Keyword(s):  
Banach Space ◽  
Efficient Solution ◽  
Multiobjective Programming ◽  
Weakly Efficient Solution ◽  
Solution Sets

scholarly journals Continuous-Time Multiobjective Optimization Problems via Invexity

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Valeriano A. De Oliveira ◽  
Marko A. Rojas-Medar
Keyword(s):  
Continuous Time ◽  
Efficient Solution ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Weakly Efficient Solution ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Relationship Of ◽  
The Relationship ◽  
Multiobjective Programming Problems

We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution to be a weakly 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 .

Painlevé–Kuratowski Convergence of Solutions for Perturbed Symmetric Set-Valued Quasi-Equilibrium Problem via Improvement Sets

2020 ◽  
Vol 37 (04) ◽  
pp. 2040003
Author(s):  
Zai-Yun Peng ◽  
Jing-Jing Wang ◽  
Xian-Jun Long ◽  
Fu-Ping Liu
Keyword(s):  
Efficient Solution ◽  
Sufficient Conditions ◽  
Quasi Equilibrium ◽  
Nonlinear Scalarization ◽  
Solution Sets ◽  
Improvement Sets ◽  
Oriented Distance ◽  
Kuratowski Convergence ◽  
Symmetric Set ◽  
Convergence Of Solution

This paper is devoted to study the Painlevé–Kuratowski convergence of solution sets for perturbed symmetric set-valued quasi-equilibrium problems (SSQEP)[Formula: see text] via improvement sets. By virtue of the oriented distance function, the sufficient conditions of Painlevé–Kuratowski convergence of efficient solution sets for (SSQEP)[Formula: see text] are obtained through a new nonlinear scalarization technical. Then, under [Formula: see text]-convergence of set-valued mappings, the Painlevé–Kuratowski convergence of weak efficient solution sets for (SSQEP)[Formula: see text] is discussed. What’s more, with suitable convergence assumptions, we also establish the sufficient conditions of lower Painlevé–Kuratowski convergence of Borwein proper efficient solution sets for (SSQEP)[Formula: see text] under improvement sets. Some interesting examples are formulated to illustrate the significance of the main results.

Properties of efficient solution sets under addition of objectives

2008 ◽  
Vol 36 (6) ◽  
pp. 718-721 ◽  
Author(s):  
Marko M. Mäkelä ◽  
Yury Nikulin
Keyword(s):  
Efficient Solution ◽  
Solution Sets

Efficient solution concepts and their application in uncertain multiobjective programming

2017 ◽  
Vol 56 ◽  
pp. 557-569 ◽  
Author(s):  
Mingfa Zheng ◽  
Yuan Yi ◽  
Zutong Wang ◽  
Tianjun Liao
Keyword(s):  
Efficient Solution ◽  
Multiobjective Programming ◽  
Solution Concepts

SENSITIVITY ANALYSIS OF WEAK EFFICIENCY IN MULTIPLE OBJECTIVE LINEAR PROGRAMMING

2011 ◽  
Vol 28 (04) ◽  
pp. 445-455 ◽  
Author(s):  
SEBASTIAN SITARZ
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Extreme Point ◽  
Efficient Solution ◽  
Multiple Objective ◽  
Weak Efficiency ◽  
Multiple Objective Linear Programming ◽  
Weakly Efficient Solution ◽  
Extreme Solutions

This paper, studies the sensitivity analysis of weakly efficient extreme solutions in multiple objective linear programming (MOLP). The aim of the paper is to compute the set of the parameters (corresponding to one coefficient) for which a given extreme point is a weakly efficient solution. We also focus on the properties of the parameters set by proving convexity and closeness of this set. Moreover, we compare the results of the sensitivity analysis of efficiency and of weak efficiency in MOLP.

scholarly journals Connectedness and Path Connectedness of Weak Efficient Solution Sets of Vector Optimization Problems via Nonlinear Scalarization Methods

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 947
Author(s):  
Xin Xu ◽  
Yang Dong Xu
Keyword(s):  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Nonlinear Scalarization ◽  
Solution Sets ◽  
Scalarization Method ◽  
Path Connectedness ◽  
Weak Efficient Solution ◽  
Efficient Solution Set

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.

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