scholarly journals The space of star-shaped sets and its applications in nonsmooth optimization

1986 ◽  
pp. 176-202 ◽  
Author(s):  
A. M. Rubinov ◽  
A. A. Yagubov
Keyword(s):  
Nonsmooth Optimization

Rapidly Convergent Algorithms for Nonsmooth Optimization.

1986 ◽  
Author(s):  
Robert Mifflin
Keyword(s):  
Nonsmooth Optimization

scholarly journals A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hamid Reza Erfanian ◽  
M. H. Noori Skandari ◽  
A. V. Kamyad
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Nonsmooth Equations ◽  
Smooth Functions ◽  
Generalized Derivative ◽  
Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

Nonsmooth Optimization Method for Image Restoration

1995 ◽  
Author(s):  
Kazufumi Ito ◽  
Karl Kunisch
Keyword(s):  
Image Restoration ◽  
Nonsmooth Optimization ◽  
Numerical Optimization ◽  
Augmented Lagrangian ◽  
Energy Criterion ◽  
Optimization Methods ◽  
Optimization Method ◽  
Augmented Lagrangian Methods ◽  
Active Set ◽  
First Order

Abstract In this paper we discuss applications of the numerical optimization methods for nonsmooth optimization, developed in [IK1] for the variational formulation of image restoration problems involving bounded variation type energy criterion. The Uzawa’s algorithm, first order augmented Lagrangian methods and Newton-like update using the active set strategy are described.

Algorithms of Nonsmooth Optimization

1998 ◽  
pp. 43-68
Author(s):  
Jiři Outrata ◽  
Michal Kočvara ◽  
Jochem Zowe
Keyword(s):  
Nonsmooth Optimization

On Generalized Second-Order Derivatives and Taylor Expansions in Nonsmooth Optimization

1994 ◽  
Vol 32 (3) ◽  
pp. 591-611 ◽  
Author(s):  
W. L. Chan ◽  
L. R. Huang ◽  
K. F. Ng
Keyword(s):  
Nonsmooth Optimization ◽  
Second Order ◽  
Taylor Expansions

scholarly journals Nonconvex nonsmooth optimization via convex–nonconvex majorization–minimization

2016 ◽  
Vol 136 (2) ◽  
pp. 343-381 ◽  
Author(s):  
A. Lanza ◽  
S. Morigi ◽  
I. Selesnick ◽  
F. Sgallari
Keyword(s):  
Nonsmooth Optimization ◽  
Nonconvex Nonsmooth Optimization
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