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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[1]  
Ansari QH(2018)Characterizations of set relations with respect to variable domination structures via oriented distance function Optimization 67 1389-1407
[2]  
Köbis E(2018)Minimal element theorems and Ekeland’s variational principle with new set order relations J Nonlinear Convex Anal 19 1127-1139
[3]  
Sharma PK(2012)Four types of nonlinear scalarizations and some applications in set optimization Nonlinear Anal 75 3821-3835
[4]  
Ansari QH(2019)A unified characterization of nonlinear scalarizing functionals in optimization Vietnam J Math 47 683-713
[5]  
Sharma PK(2017)Characterizations of set order relations and constrained set optimization problems via oriented distance function Optimization 66 1741-1754
[6]  
Yao JC(2006)First order optimality conditions in set-valued optimization Math Methods Oper Res 63 87-106
[7]  
Araya Y(2010)Lagrange multipliers for J Optim Theory Appl 145 196-211
[8]  
Bouza G(1990)-Pareto solutions in vector optimization with non solid cones in Banach spaces J Optim Theory Appl 67 297-320
[9]  
Quintana E(2015)Nonconvex separation theorems and some applications in vector optimization J Global Optim 61 525-552
[10]  
Tammer C(2005)Scalarization in set optimization with solid and nonsolid ordering cones J Math Anal Appl 311 647-663
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