Path connectedness of the efficient solution set for generalized vector quasi-equilibrium problems

2021 ◽  
Author(s):  
Chong Cui ◽  
Shengjie Li
Keyword(s):  
Efficient Solution ◽  
Equilibrium Problems ◽  
Solution Set ◽  
Quasi Equilibrium ◽  
Path Connectedness ◽  
Efficient Solution Set

scholarly journals Existence and Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Kaihong Wang ◽  
Wenyan Zhang ◽  
Min Fang
Keyword(s):  
Existence Result ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Solution Set ◽  
Quasi Equilibrium ◽  
Well Posedness

An existence result for the solution set of symmetric vector quasi-equilibrium problems that allows for discontinuities is obtained. Moreover, sufficient conditions for the generalized Levitin-Polyak well-posedness of symmetric vector quasi-equilibrium problems are established.

scholarly journals S-strictly quasi-concave vector maximisation

2003 ◽  
Vol 67 (3) ◽  
pp. 429-443
Author(s):  
Hong-Bin Dong ◽  
Xun-Hua Gong ◽  
Shou-Yang Wang ◽  
Luis Coladas
Keyword(s):  
Vector Space ◽  
Efficient Solution ◽  
Vector Lattice ◽  
Solution Set ◽  
Multiple Objective ◽  
Objective Space ◽  
Vector Valued Function ◽  
The Relationship ◽  
Vector Valued ◽  
Efficient Solution Set

In this paper, we discuss the relationship among the concepts of an S-strictly quasiconcave vector-valued function introduced by Benson and Sun, a C-strongly quasiconcave vector-valued function and a C-strictly quasiconcave vector-valued function in a topological vector space with a lattice ordering. We generalize a main result obtained by Benson and Sun about the closedness of an efficient solution set in multiple objective programming. We prove that an efficient solution set is closed and connected when the objective function is a continuous S-strictly quasiconcave vector-valued function, the objective space is a topological vector lattice and the ordering cone has a nonempty interior.

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 The Taxation of Environmental Pollution: A Model for Tax Revenue-Environmental Quality Tradeoffs

2016 ◽  
Vol 8 (1) ◽  
pp. 65
Author(s):  
Hung-Ming Peter Wu ◽  
Keith D. Willett
Keyword(s):  
Environmental Quality ◽  
Efficient Solution ◽  
Cost Model ◽  
Solution Set ◽  
Tax Revenue ◽  
Optimal Point ◽  
Tax Rate ◽  
Optimal Tax ◽  
Multi Objective Programming ◽  
Efficient Solution Set

The paper analyzes the Willamette River in Oregon. Here a model (combining the least-cost model and the constraint method of multi-objective programming) is used to determine the appropriate tax rate on environmental externalities, incorporating both revenue and environmental quality objectives. The study finds the following. (1) By using the optimal tax rate, the appropriate tax revenue is determined. (2) The efficient solution set (including tax revenue and water quality considerations) is found by using differing optimal tax rates. (3) The optimal point (solution) in the efficient solution set is chosen by the geometrical argument approach and trade-off analysis approach.

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