Contingent derivative of the perturbation map in multiobjective optimization

1991 ◽  
Vol 70 (2) ◽  
pp. 385-396 ◽  
Author(s):  
D. S. Shi
Keyword(s):  
Multiobjective Optimization ◽  
Contingent Derivative ◽  
Perturbation Map

Second-Order Composed Contingent Derivative of the Perturbation Map in Multiobjective Optimization

2020 ◽  
Vol 37 (02) ◽  
pp. 2050002
Author(s):  
Zhenhua Peng ◽  
Zhongping Wan
Keyword(s):  
Second Order ◽  
Contingent Derivative ◽  
Lipschitz Property ◽  
Dini Derivative ◽  
New Concepts ◽  
Locally Lipschitz ◽  
Perturbation Maps ◽  
Perturbation Map ◽  
First Time ◽  
Derivatives Of

In view of the structural advantage of second-order composed derivatives, the purpose of this paper is to analyze quantitatively the behavior of perturbation maps for the first time by using this concept. First, new concepts of the second-order composed adjacent derivative and the second-order composed lower Dini derivative are introduced. Some relationships among the second-order composed contingent derivative, the second-order composed adjacent derivative and the second-order composed lower Dini derivative are discussed. Second, the relationships between second-order composed lower Dini derivable and Aubin property are provided. Third, by virtue of second-order composed contingent derivatives and the above relationships, some results concerning second-order sensitivity analysis are established without the assumption of the locally Lipschitz property or the locally Hölder continuity. Finally, we give some complete characterizations of second-order composed contingent derivatives of the perturbation maps.

scholarly journals Higher-order variational set of the benson proper perturbation map in set-valued optimization

2020 ◽  
Vol 3 (4) ◽  
pp. 279-285
Author(s):  
Linh Manh Ha
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Problem ◽  
Research Direction ◽  
Higher Order ◽  
Contingent Derivative ◽  
Optimal Value ◽  
Objective Space ◽  
The World ◽  
Variational Sets ◽  
Perturbation Map

In the paper, we study sensitivity analysis in set-valued optimization, a research direction has been attracting much attention of many mathematicians in the world recently. The main derivative used in the paper is higher-order variational set (introduced by Khanh and Tuan in 2008) which is considered as a generalization of the contingent derivative (known as the first and the most popular derivative in set-valued optimization). Firstly, we establish relationships between higher-order variational sets of a given set-valued map and those of its profile (extended by a ordering cone). Then, we give results on higher-order variational set of the Benson proper perturbation map for a kind of set-valued optimization problem, the perturbation map is defined in the objective space. Finally, we apply the obtained results to sensitivity analysis for optimal-value map of a parametrized constrained set-valued optimization problem whose the objective map and constrained maps depends on some parameter. More precisely, some results on sensitivity analysis for parametrized constrained set-valued optimization problem are obtained. The content of the paper gives us more applications of higher-order variational set in set-valued optimization.  

Multiobjective Optimization of Plate-Fin Heat Exchanger by Tsallis Differential Evolution

2017 ◽  
Author(s):  
Viviana Mariani ◽  
Leandro Coelho ◽  
Emerson Hochsteiner de Vasconcelos Segundo
Keyword(s):  
Heat Exchanger ◽  
Multiobjective Optimization ◽  
Differential Evolution
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