scholarly journals Necessary Conditions for Weak Sharp Minima in Cone-Constrained Optimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
W. Y. Zhang ◽  
S. Xu ◽  
S. J. Li
Keyword(s):  
Normal Cone ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Necessary Condition ◽  
Directional Derivatives ◽  
Weak Sharp Minima ◽  
Dini Directional Derivatives ◽  
Cone Constrained Optimization ◽  
Weak Sharp ◽  
Sharp Minima

We study weak sharp minima for optimization problems with cone constraints. Some necessary conditions for weak sharp minima of higher order are established by means of upper Studniarski or Dini directional derivatives. In particular, when the objective and constrained functions are strict derivative, a necessary condition is obtained by a normal cone.

Weak Sharp Minima for Convex Infinite Optimization Problems in Normed Linear Spaces

2018 ◽  
Vol 28 (3) ◽  
pp. 1999-2021
Author(s):  
Chong Li ◽  
Li Meng ◽  
Lihui Peng ◽  
Yaohua Hu ◽  
Jen-Chih Yao
Keyword(s):  
Optimization Problems ◽  
Linear Spaces ◽  
Weak Sharp Minima ◽  
Normed Linear Spaces ◽  
Weak Sharp ◽  
Sharp Minima

scholarly journals Weak Sharp Minima in Set-Valued Optimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Ming-hao Jin ◽  
Jun-xiang Wang ◽  
Shu Xu
Keyword(s):  
Necessary Conditions ◽  
Optimization Problems ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Outer Limit ◽  
Sufficient And Necessary Conditions ◽  
Scalarization Function ◽  
Weak Sharp ◽  
Sharp Minima

We introduce the notion of a weakψ-sharp minimizer for set-valued optimization problems. We present some sufficient and necessary conditions that a pair point is a weakψ-sharp minimizer through the outer limit of set-valued map and develop the characterization of the weakψ-sharp minimizer in terms of a generalized nonlinear scalarization function. These results extend the corresponding ones in Studniarski (2007).

New characterizations of weak sharp minima

2011 ◽  
Vol 6 (8) ◽  
pp. 1773-1785 ◽  
Author(s):  
Jinchuan Zhou ◽  
Changyu Wang
Keyword(s):  
Weak Sharp Minima ◽  
Weak Sharp ◽  
Sharp Minima
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