Scalarizing Functions for Generating the Weakly Efficient Solution Set in Convex Multiobjective Problems

2005 ◽  
Vol 15 (4) ◽  
pp. 987-1001 ◽  
Author(s):  
Dinh The Luc ◽  
Thai Quynh Phong ◽  
Michel Volle
Keyword(s):  
Efficient Solution ◽  
Solution Set ◽  
Weakly Efficient Solution ◽  
Multiobjective Problems ◽  
Efficient Solution Set

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 .

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 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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