Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization

被引：0
作者：
L. Huerga
B. Jiménez
V. Novo
A. Vílchez
机构：
[1] E.T.S.I. Industriales,Departamento de Matemática Aplicada
[2] Universidad Nacional de Educación a Distancia,undefined
[3] Ciudad Universitaria,undefined
来源：
Mathematical Methods of Operations Research | 2021年 / 93卷
关键词：
Oriented distance; Set optimization; Set order relations; Scalarization in set optimization; Convexity; Continuity; Lagrange multipliers; 06A75; 49J53; 90C29;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the setting of normed spaces ordered by a convex cone not necessarily solid, we use six set scalarization functions, which are extensions of the oriented distance of Hiriart-Urruty, and we discuss convexity and continuity properties of their composition with two set-valued maps. Furthermore, as an application, we derive a multiplier rule for weak minimal solutions of a convex set optimization problem, with respect to the lower set less preorder of Kuroiwa. Some illustrative examples are also given.
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页码：413 / 436
页数：23
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[11]  
Chen J(2018)Lagrange multipliers for set-valued optimization problems associated with coderivatives Optimization 67 1031-1050
[12]  
Ansari QH(2010)A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization SIAM J Financ Math 1 66-95
[13]  
Yao JC(2019)Duality for set-valued measures of risk Optimization 68 1685-1718
[14]  
Crespi GP(2018)Nonlinear scalarizing functions in set optimization problems J Optim Theory Appl 177 679-695
[15]  
Ginchev I(2017)Continuity and convexity of a nonlinear scalarizing function in set optimization problems with applications Optimization 66 1273-1289
[16]  
Rocca M(2007)Some useful set-valued maps in set optimization J Math Anal Appl 325 1-18
[17]  
Durea M(1979)Nonconvex scalarization in set optimization with set-valued maps Math Oper Res 4 79-97
[18]  
Dutta J(2011)Tangent cones, generalized gradients and mathematical programming in Banach spaces J Optim Theory Appl 148 209-236
[19]  
Tammer C(2018)New order relations in set optimization Optimization 67 2091-2116
[20]  
Gerth C(2020)A set scalarization function based on the oriented distance and relations with other set scalarizations Math Methods Oper Res 91 89-115
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