Nonlinear scalarization functions and polar cone in set optimization

2016 ◽  
Vol 11 (3) ◽  
pp. 521-535 ◽  
Author(s):  
S. Khoshkhabar-amiranloo ◽  
E. Khorram ◽  
M. Soleimani-damaneh
Keyword(s):  
Set Optimization ◽  
Nonlinear Scalarization ◽  
Polar Cone

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.

Qualitative properties of solutions to set optimization problems

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Lam Quoc Anh ◽  
Nguyen Huu Danh ◽  
Pham Thanh Duoc ◽  
Tran Ngoc Tam
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Qualitative Properties ◽  
Qualitative Properties Of Solutions

scholarly journals Lagrange Duality in Set Optimization

2013 ◽  
Vol 161 (2) ◽  
pp. 368-397 ◽  
Author(s):  
Andreas H. Hamel ◽  
Andreas Löhne
Keyword(s):  
Set Optimization ◽  
Lagrange Duality

scholarly journals Semicontinuity of the Solution Mapping to a Parametric Generalized Weak Ky Fan Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Y. D. Xu
Keyword(s):  
Lower Semicontinuity ◽  
Solution Set ◽  
Ky Fan Inequality ◽  
Nonlinear Scalarization ◽  
Solution Mapping ◽  
Ky Fan ◽  
Upper And Lower Semicontinuity

Under new assumptions, which do not contain any information about the solution set, the upper and lower semicontinuity of the solution mapping to a class of parametric generalized weak Ky Fan inequality are established by using a nonlinear scalarization technique. These results extend and improve the recent ones in the literature. Some examples are given to illustrate our results.

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