Globally convergent methods for n-dimensional multiextremal optimization

Optimization ◽  
1986 ◽  
Vol 17 (2) ◽  
pp. 187-202 ◽  
Author(s):  
J. Pintér
Keyword(s):  
Globally Convergent ◽  
Globally Convergent Methods ◽  
Multiextremal Optimization

scholarly journals New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permittingf′(xn)=0

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Ramandeep Behl ◽  
V. Kanwar
Keyword(s):  
Higher Order ◽  
The Other ◽  
Robust Methods ◽  
Challenging Problem ◽  
Order Convergence ◽  
Dynamical Study ◽  
Globally Convergent ◽  
Special Cases ◽  
Globally Convergent Methods ◽  
Ostrowski’S Method

Construction of higher-order optimal and globally convergent methods for computing simple roots of nonlinear equations is an earliest and challenging problem in numerical analysis. Therefore, the aim of this paper is to present optimal and globally convergent families of King's method and Ostrowski's method having biquadratic and eight-order convergence, respectively, permittingf′(x)=0in the vicinity of the required root. Fourth-order King's family and Ostrowski's method can be seen as special cases of our proposed scheme. All the methods considered here are found to be more effective to the similar robust methods available in the literature. In their dynamical study, it has been observed that the proposed methods have equal or better stability and robustness as compared to the other methods.

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

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