Sequential Penalty Derivative-Free Methods for Nonlinear Constrained Optimization

2010 ◽  
Vol 20 (5) ◽  
pp. 2614-2635 ◽  
Author(s):  
Giampaolo Liuzzi ◽  
Stefano Lucidi ◽  
Marco Sciandrone
Keyword(s):  
Constrained Optimization ◽  
Nonlinear Constrained Optimization ◽  
Derivative Free ◽  
Derivative Free Methods

A penalty derivative-free algorithm for nonlinear constrained optimization

2014 ◽  
Vol 9 (6) ◽  
pp. 1213-1229
Author(s):  
Wei Lv ◽  
Qiang Sun ◽  
He Lin ◽  
Ruirui Sui
Keyword(s):  
Constrained Optimization ◽  
Nonlinear Constrained Optimization ◽  
Derivative Free

An efficient class of fourth-order derivative-free method for multiple-roots

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sunil Kumar ◽  
Deepak Kumar ◽  
Janak Raj Sharma ◽  
Ioannis K. Argyros
Keyword(s):  
Multiple Root ◽  
Second Step ◽  
Optimal Order ◽  
Multiple Roots ◽  
Nonlinear Functions ◽  
New Methods ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Derivative Free Method ◽  
Good Number

Abstract Many optimal order multiple root techniques, which use derivatives in the algorithm, have been proposed in literature. Many researchers tried to construct an optimal family of derivative-free methods for multiple roots, but they did not get success in this direction. With this as a motivation factor, here, we present a new optimal class of derivative-free methods for obtaining multiple roots of nonlinear functions. This procedure involves Traub–Steffensen iteration in the first step and Traub–Steffensen-like iteration in the second step. Efficacy is checked on a good number of relevant numerical problems that verifies the efficient convergent nature of the new methods. Moreover, we find that the new derivative-free methods are just as competent as the other existing robust methods that use derivatives.

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