On Generalized Pseudo- and Quasiconvexities for Nonsmooth Functions

2018 ◽  
pp. 129-155
Author(s):  
Ville-Pekka Eronen ◽  
Marko M. Mäkelä ◽  
Napsu Karmitsa
Keyword(s):  
Nonsmooth Functions

scholarly journals Algebraic Univalence Theorems for Nonsmooth Functions

2000 ◽  
Vol 252 (2) ◽  
pp. 917-935 ◽  
Author(s):  
M.Seetharama Gowda ◽  
G Ravindran
Keyword(s):  
Nonsmooth Functions

Characterization of nonsmooth functions through their generalized gradients

Optimization ◽  
1991 ◽  
Vol 22 (3) ◽  
pp. 401-416 ◽  
Author(s):  
R. Ellaia ◽  
A. Hassouni
Keyword(s):  
Generalized Gradients ◽  
Nonsmooth Functions

scholarly journals The Boosted Difference of Convex Functions Algorithm for Nonsmooth Functions

2020 ◽  
Vol 30 (1) ◽  
pp. 980-1006 ◽  
Author(s):  
Francisco J. Aragón Artacho ◽  
Phan T. Vuong
Keyword(s):  
Convex Functions ◽  
Nonsmooth Functions ◽  
Difference Of Convex Functions ◽  
Difference Of Convex

On Lipschitz behaviour of some generalized derivatives

2013 ◽  
Vol 63 (3) ◽  
Author(s):  
Dušan Bednařík ◽  
Karel Pastor
Keyword(s):  
Reference Point ◽  
Clarke Subdifferential ◽  
Generalized Derivatives ◽  
Lipschitz Property ◽  
Dini Derivative ◽  
Stable Property ◽  
Nonsmooth Functions ◽  
Clarke Derivative

AbstractThe aim of the present paper is to compare various forms of stable properties of nonsmooth functions at some points. By stable property we mean the Lipschitz property of some generalized derivatives related only to the reference point. Namely we compare Lipschitz behaviour of lower Clarke derivative, lower Dini derivative and calmness of Clarke subdifferential. In this way, we continue our study of λ-stable functions.

On Characterizations ofP- andP0-Properties in Nonsmooth Functions

2000 ◽  
Vol 25 (3) ◽  
pp. 400-408 ◽  
Author(s):  
Yoon Song ◽  
M. Seetharama Gowda ◽  
G. Ravindran
Keyword(s):  
Nonsmooth Functions

scholarly journals A conjugate gradient algorithm and its application in large-scale optimization problems and image restoration

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Gonglin Yuan ◽  
Tingting Li ◽  
Wujie Hu
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Trust Region ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Smooth Functions ◽  
Nonsmooth Functions ◽  
Large Scale Unconstrained Optimization

Abstract To solve large-scale unconstrained optimization problems, a modified PRP conjugate gradient algorithm is proposed and is found to be interesting because it combines the steepest descent algorithm with the conjugate gradient method and successfully fully utilizes their excellent properties. For smooth functions, the objective algorithm sufficiently utilizes information about the gradient function and the previous direction to determine the next search direction. For nonsmooth functions, a Moreau–Yosida regularization is introduced into the proposed algorithm, which simplifies the process in addressing complex problems. The proposed algorithm has the following characteristics: (i) a sufficient descent feature as well as a trust region trait; (ii) the ability to achieve global convergence; (iii) numerical results for large-scale smooth/nonsmooth functions prove that the proposed algorithm is outstanding compared to other similar optimization methods; (iv) image restoration problems are done to turn out that the given algorithm is successful.

scholarly journals Using simplex gradients of nonsmooth functions in direct search methods

2008 ◽  
Vol 28 (4) ◽  
pp. 770-784 ◽  
Author(s):  
A. L. Custodio ◽  
J. E. Dennis ◽  
L. N. Vicente
Keyword(s):  
Direct Search ◽  
Search Methods ◽  
Direct Search Methods ◽  
Nonsmooth Functions
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