scholarly journals Appendix 3: Systems with Explicit and Implicit Generalized Derivative

2014 ◽  
pp. 277-300
Keyword(s):  
Generalized Derivative

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.

Generalized derivative and π-derivative for set-valued functions

2011 ◽  
Vol 181 (11) ◽  
pp. 2177-2188 ◽  
Author(s):  
Y. Chalco-Cano ◽  
H. Román-Flores ◽  
M.D. Jiménez-Gamero
Keyword(s):  
Generalized Derivative

Lanczos' Generalized Derivative

1998 ◽  
Vol 105 (4) ◽  
pp. 320-326 ◽  
Author(s):  
C. W. Groetsch
Keyword(s):  
Generalized Derivative

scholarly journals Differential Subordination with Generalized Derivative Operator of Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Entisar El-Yagubi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Generalized Derivative

Motivated by generalized derivative operator defined by the authors (El-Yagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator Dλ1,λ2,δm,b are given.

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