scholarly journals Structure of Pareto Solutions of Generalized Polyhedral-Valued Vector Optimization Problems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Qinghai He ◽  
Weili Kong
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Solution Set ◽  
Pareto Optimal ◽  
Pareto Solution ◽  
Value Set ◽  
Set Valued Mapping ◽  
Optimal Value

In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.

scholarly journals Generalized Stampacchia Vector Variational-Like Inequalities and Vector Optimization Problems Involving Set-Valued Maps

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yanfei Chai ◽  
Sanyang Liu ◽  
Guotao Wang
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problem ◽  
Gap Functions ◽  
Weak Formulation ◽  
Existence Of A Solution ◽  
Weakly Efficient Solutions ◽  
Set Valued Mapping ◽  
Finite Dimensional

We first obtain that subdifferentials of set-valued mapping from finite-dimensional spaces to finite-dimensional possess certain relaxed compactness. Then using this weak compactness, we establish gap functions for generalized Stampacchia vector variational-like inequalities which are defined by means of subdifferentials. Finally, an existence result of generalized weakly efficient solutions for vector optimization problem involving a subdifferentiable and preinvex set-valued mapping is established by exploiting the existence of a solution for the weak formulation of the generalized Stampacchia vector variational-like inequality via a Fan-KKM lemma.

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 Sensitivity analysis for parametric vector optimization problems using differential equations approach

2001 ◽  
Vol 25 (9) ◽  
pp. 621-628
Author(s):  
Fatma M. Ali
Keyword(s):  
Differential Equations ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Parametric Vector Optimization ◽  
Local Solutions

A new method for obtaining sensitivity information for parametric vector optimization problems(VOP)vis presented, where the parameters in the objective functions and anywhere in the constraints. This method depends on using differential equations technique for solving multiobjective nonlinear programing problems which is very effective in finding many local Pareto optimal solutions. The behavior of the local solutions for slight perturbation of the parameters in the neighborhood of their chosen initial values is presented by using the technique of trajectory continuation. Finally some examples are given to show the efficiency of the proposed method.

Higher order duality for cone vector optimization problems

2018 ◽  
Vol 13 (01) ◽  
pp. 2050020
Author(s):  
Vivek Singh ◽  
Anurag Jayswal ◽  
S. Al-Homidan ◽  
I. Ahmad
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Strong Duality ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Support Functions ◽  
Invex Functions ◽  
New Class ◽  
Duality Results ◽  
Higher Order Duality

In this paper, we present a new class of higher order [Formula: see text]-[Formula: see text]-invex functions over cones. Further, we formulate two types of higher order dual models for a vector optimization problem over cones containing support functions in objectives as well as in constraints and establish several duality results, viz., weak and strong duality results.

A collaborative design method for satellite module component assignment and layout optimization

2019 ◽  
Vol 233 (15) ◽  
pp. 5471-5491
Author(s):  
Feng-Zhe Cui ◽  
Chong-Quan Zhong ◽  
Xiu-Kun Wang ◽  
Hong-Fei Teng
Keyword(s):  
Collaborative Design ◽  
Optimization Design ◽  
Optimization Problems ◽  
Design Method ◽  
Layout Optimization ◽  
Solution Set ◽  
Pareto Solution ◽  
Multi Objective ◽  
Component Layout ◽  
Assignment Scheme

The collaborative design of the multi-module satellite component (equipment) assignment and layout is the key aspect of the overall satellite design, and the two parts are closely related. In the past, satellite module component layout optimization usually adopted fixed component assignments, which remained constant in the layout optimization stage. If the components were improperly distributed in these modules, it would seriously affect the layout optimization. To overcome this disadvantage, a collaborative design method for the component assignment and layout design is presented for the multi-module (or multi-bearing plate) satellite component layout problem, based on a multi-agent system. First, the component assignment agent adopted a multi-objective optimization method (the non-dominated sorting genetic algorithm II, NSGA-II) to obtain the approximate Pareto solution set of the satellite component assignment scheme. Second, it adopted a fuzzy multi-objective decision method to select a high-quality component assignment scheme from the approximate Pareto solution set. Third, the layout agent employed a dual system co-evolutionary method for the layout optimization design. In the process of the layout optimization, the layout result is fed back to the component assignment design, and the component assignment is adjusted according to the result of the layout optimization. Thus, the above process is continually iterated to achieve the optimal collaborative design of the component assignment and the layout. The proposed method is applied to a simplified multi-module satellite component assignment and layout optimization problem and aims to provide a reference and technical support for other similar multi-module equipment assignment and layout optimization problems.

scholarly journals Coderivatives and Aubin property of efficient point and efficient solution set-valued maps in parametric vector optimization

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaowei Xue
Keyword(s):  
Explicit Expression ◽  
Vector Optimization ◽  
Efficient Solution ◽  
Vector Optimization Problem ◽  
Solution Set ◽  
Efficient Point ◽  
Aubin Property ◽  
Parametric Vector Optimization ◽  
Whole Space ◽  
Efficient Solution Set

Abstract The aim of this paper is computing the coderivatives of efficient point and efficient solution set-valued maps in a parametric vector optimization problem. By using a method different from the existing literature we establish an upper estimate and explicit expression for the coderivatives of an efficient point set-valued map where the independent variable can take values in the whole space. As an application, we give some characterizations on the Aubin property of an efficient point map and an explicit expression of the coderivative for an efficient solution map. We provide several examples illustrating the main results.

scholarly journals A class of semilocal E-preinvex maps in Banach spaces with applications to nondifferentiable vector optimization

2013 ◽  
Vol 4 (1) ◽  
pp. 1-10
Author(s):  
Hehua Jiao
Keyword(s):  
Optimality Conditions ◽  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Basic Properties ◽  
New Class ◽  
Duality Results

In this paper, a new class of semilocal E-preinvex and related maps in Banach spaces is introduced for a nondifferentiable vector optimization problem with restrictions of inequalities and some of its basic properties are studied. Furthermore, as its applications, some optimality conditions and duality results are established for a nondifferentiable vector optimization under the aforesaid maps assumptions.

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