Levitin–Polyak well-posedness for set optimization problems involving set order relations

Positivity ◽  
2018 ◽  
Vol 23 (3) ◽  
pp. 599-616 ◽  
Author(s):  
Pham Thi Vui ◽  
Lam Quoc Anh ◽  
Rabian Wangkeeree
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Well Posedness ◽  
Order Relations ◽  
Set Order Relations

Well-Posedness for Set Optimization Problems Involving Set Order Relations

2020 ◽  
Vol 45 (2) ◽  
pp. 329-344
Author(s):  
Pham Thi Vui ◽  
Lam Quoc Anh ◽  
Rabian Wangkeeree
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Well Posedness ◽  
Order Relations ◽  
Set Order Relations

Scalarization and pointwise well-posedness for set optimization problems

2015 ◽  
Vol 62 (4) ◽  
pp. 763-773 ◽  
Author(s):  
Xian-Jun Long ◽  
Jian-Wen Peng ◽  
Zai-Yun Peng
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Well Posedness

scholarly journals Scalarization and well-posedness for set optimization using coradiant sets

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3457-3471
Author(s):  
Bin Yao ◽  
Sheng Li
Keyword(s):  
Optimization Problem ◽  
Set Optimization ◽  
Well Posedness ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalar Optimization ◽  
Set Optimization Problem ◽  
Order Relations ◽  
Scalarization Function

The aim of this paper is to study scalarization and well-posedness for a set-valued optimization problem with order relations induced by a coradiant set. We introduce the notions of the set criterion solution for this problem and obtain some characterizations for these solutions by means of nonlinear scalarization. The scalarization function is a generalization of the scalarization function introduced by Khoshkhabar-amiranloo and Khorram. Moveover, we define the pointwise notions of LP well-posedness, strong DH-well-posedness and strongly B-well-posedness for the set optimization problem and characterize these properties through some scalar optimization problem based on the generalized nonlinear scalarization function respectively.

scholarly journals Well-posedness for set optimization problems

2009 ◽  
Vol 71 (9) ◽  
pp. 3769-3778 ◽  
Author(s):  
W.Y. Zhang ◽  
S.J. Li ◽  
K.L. Teo
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Well Posedness
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