scholarly journals Second-Order Optimality Conditions for Set-Valued Optimization Problems Under Benson Proper Efficiency

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Qilin Wang ◽  
Guolin Yu
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Second Order ◽  
Proper Efficiency ◽  
Second Order Optimality Conditions ◽  
Benson Proper Efficiency ◽  
Necessary And Sufficient ◽  
Proper Efficient Solutions

Some new properties are obtained for generalized second-order contingent (adjacent) epiderivatives of set-valued maps. By employing the generalized second-order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set-valued optimization problems. The results obtained improve the corresponding results in the literature.

New second-order radial epiderivatives and applications to optimality conditions

2020 ◽  
Vol 54 (4) ◽  
pp. 949-959
Author(s):  
Xiaoyan Zhang ◽  
Qilin Wang
Keyword(s):  
Optimality Conditions ◽  
Recent Literature ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Efficient Solutions ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Contingent Epiderivative ◽  
Proper Efficient Solutions

In this paper, we introduce the second-order weakly composed radial epiderivative of set-valued maps, discuss its relationship to the second-order weakly composed contingent epiderivative, and obtain some of its properties. Then we establish the necessary optimality conditions and sufficient optimality conditions of Benson proper efficient solutions of constrained set-valued optimization problems by means of the second-order epiderivative. Some of our results improve and imply the corresponding ones in recent literature.

scholarly journals Second order optimality conditions for mathematical prograramming with set functions

1985 ◽  
Vol 26 (3) ◽  
pp. 284-292 ◽  
Author(s):  
J. H. Chou ◽  
Wei-Shen Hsia ◽  
Tan-Yu Lee
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Measurable Subset ◽  
Second Order ◽  
Optimal Selection ◽  
Local Convexity ◽  
Necessary And Sufficient ◽  
Set Function ◽  
Selection Of

AbstractSecond order necessary and sufficient conditions are given for a class of optimization problems involving optimal selection of a measurable subset from a given measure subspace subject to set function inequalities. Relations between twice-differentiability at Ω and local convexity at Ω are also discussed.

scholarly journals On generalized derivatives forC1,1vector optimization problems

2003 ◽  
Vol 2003 (7) ◽  
pp. 365-376 ◽  
Author(s):  
Davide La Torre
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Vector Optimization Problems ◽  
Directional Derivatives ◽  
Generalized Derivatives ◽  
Second Order Optimality Conditions

We introduce generalized definitions of Peano and Riemann directional derivatives in order to obtain second-order optimality conditions for vector optimization problems involvingC1,1data. We show that these conditions are stronger than those in literature obtained by means of second-order Clarke subdifferential.

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