“Stochastic Nonsmooth Analysis And Optimization In Banach Spaces”

1985 ◽  
pp. 226-242
Author(s):  
Nikolaos S. Papageoraiou
Keyword(s):  
Banach Spaces ◽  
Nonsmooth Analysis ◽  
Optimization In Banach Spaces

Generalized representer theorems in Banach spaces

2019 ◽  
Vol 19 (01) ◽  
pp. 125-146
Author(s):  
Liren Huang ◽  
Chunguang Liu ◽  
Lulin Tan ◽  
Qi Ye
Keyword(s):  
Banach Spaces ◽  
Nonsmooth Analysis ◽  
Reproducing Kernel ◽  
Sparse Representations ◽  
Training Data ◽  
Loss Functions ◽  
Learning Models ◽  
Reproducing Kernel Banach Spaces

In this paper, we generalize the representer theorems in Banach spaces by the theory of nonsmooth analysis. The generalized representer theorems assure that the regularized learning models can be constructed by the nonconvex loss functions, the generalized training data, and the general Banach spaces which are nonreflexive, nonstrictly convex, and nonsmooth. Specially, the sparse representations of the regularized learning in 1-norm reproducing kernel Banach spaces are shown by the generalized representer theorems.

Convexity and Optimization in Banach Spaces (V. Barbu and Th. Precipanu)

SIAM Review ◽  
1980 ◽  
Vol 22 (3) ◽  
pp. 375-376 ◽  
Author(s):  
Richard F. Datko
Keyword(s):  
Banach Spaces ◽  
Optimization In Banach Spaces

Convexity and Optimization in Banach Spaces

2012 ◽  
Author(s):  
Viorel Barbu ◽  
Teodor Precupanu
Keyword(s):  
Banach Spaces ◽  
Optimization In Banach Spaces
Sign in / Sign up

Export Citation Format

Share Document