Subdifferential set of the supremum of lower semi-continuous convex functions and the conical hull intersection property

Top ◽  
2006 ◽  
Vol 14 (2) ◽  
pp. 355-374 ◽  
Author(s):  
A. Hantoute
Keyword(s):  
Convex Functions ◽  
Intersection Property ◽  
Lower Semi ◽  
Conical Hull

scholarly journals A note on convex functions

1999 ◽  
Vol 22 (3) ◽  
pp. 525-534 ◽  
Author(s):  
Yu-Ru Syau
Keyword(s):  
Continuous Function ◽  
Euclidean Space ◽  
Convex Function ◽  
Convex Functions ◽  
Dimensional Euclidean Space ◽  
Strictly Convex ◽  
Lower Semi

In this paper, we give two weak conditions for a lower semi-continuous function on then-dimensional Euclidean spaceRnto be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions.

scholarly journals Analytic characterizations of Mazurʼs intersection property via convex functions

2012 ◽  
Vol 262 (11) ◽  
pp. 4731-4745 ◽  
Author(s):  
Lizhen Chen ◽  
Lixin Cheng
Keyword(s):  
Convex Functions ◽  
Intersection Property

scholarly journals Iterative methods for optimization problems and image restoration

2021 ◽  
Vol 37 (3) ◽  
pp. 497-512
Author(s):  
ANANTACHAI PADCHAROEN ◽  
◽  
DUANGKAMON KITKUAN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Image Restoration ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Minimization Problem ◽  
Convex Functions ◽  
Optimization Problems ◽  
Nonexpansive Mappings ◽  
Lower Semi

In this paper, we introduce a new accelerated iterative method for finding a common fixed point of a countable family of nonexpansive mappings in the Hilbert spaces framework. Using our main result, we obtain a new accelerated image restoration iterative method for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply our algorithm to solving image restoration problems.

The strong conical hull intersection property for convex programming

2005 ◽  
Vol 106 (1) ◽  
pp. 81-92 ◽  
Author(s):  
V. Jeyakumar
Keyword(s):  
Convex Programming ◽  
Intersection Property ◽  
Conical Hull

Fenchel Duality and the Strong Conical Hull Intersection Property

1999 ◽  
Vol 102 (3) ◽  
pp. 681-695 ◽  
Author(s):  
F. Deutsch ◽  
W. Li ◽  
J. Swetits
Keyword(s):  
Intersection Property ◽  
Fenchel Duality ◽  
Conical Hull

Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization

1999 ◽  
Vol 86 (1) ◽  
pp. 135-160 ◽  
Author(s):  
Heinz H. Bauschke ◽  
Jonathan M. Borwein ◽  
Wu Li
Keyword(s):  
Convex Optimization ◽  
Error Bounds ◽  
Intersection Property ◽  
Bounded Linear ◽  
Linear Regularity ◽  
Conical Hull

scholarly journals Monotone Valuations on the Space of Convex Functions

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
L. Cavallina ◽  
A. Colesanti
Keyword(s):  
Convex Functions ◽  
Integral Representations ◽  
Lower Semi ◽  
Rigid Motions

Abstract We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.

Generalized Uniformly Close-to-Convex Functions of Order gamma and Type beta

2015 ◽  
Vol 1 (1042) ◽  
Author(s):  
F.M. Al-Oboudi
Keyword(s):  
Convex Functions

Generalization of Favard’s and Berwald’s Inequalities for Strongly Convex Functions

2019 ◽  
Vol 10 (4) ◽  
Author(s):  
Muhammad Adil Khan ◽  
Syed Zaheer Ullah ◽  
Yuming Chu
Keyword(s):  
Convex Functions ◽  
Strongly Convex Functions ◽  
Strongly Convex
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