An algorithm for the total, or partial, factorization of a polynomial

1977 ◽  
Vol 82 (3) ◽  
pp. 427-437 ◽  
Author(s):  
M. R. Farmer ◽  
G. Loizou
Keyword(s):  
Numerical Results ◽  
Search Procedure ◽  
Multiple Zeros ◽  
Globally Convergent ◽  
Simultaneous Iteration ◽  
Accelerate Convergence ◽  
Iteration Function ◽  
Convergent Algorithm

AbstractA globally convergent algorithm is presented for the total, or partial, factorization of a polynomial. Firstly, a circle is found containing all the zeros. Secondly, a search procedure locates smaller circles, each containing a zero, and the multiplicities are then calculated. Thirdly, a simultaneous Iteration Function is used to accelerate convergence. The Iteration Function is chosen from a class of such functions derived herein to deal with the general case of multiple zeros; various properties of these functions are also discussed. Finally, sample numerical results are given which demon-strate the effectiveness of the algorithm.

A Penalty-Free Method with Trust Region for Nonlinear Semidefinite Programming

2015 ◽  
Vol 32 (01) ◽  
pp. 1540006 ◽  
Author(s):  
Zhongwen Chen ◽  
Shicai Miao
Keyword(s):  
Semidefinite Programming ◽  
Objective Function ◽  
Penalty Function ◽  
Trust Region ◽  
Numerical Results ◽  
New Method ◽  
Penalty Parameter ◽  
Nonlinear Semidefinite Programming ◽  
Globally Convergent ◽  
Nonlinear Objective Function

In this paper, we propose a class of new penalty-free method, which does not use any penalty function or a filter, to solve nonlinear semidefinite programming (NSDP). So the choice of the penalty parameter and the storage of filter set are avoided. The new method adopts trust region framework to compute a trial step. The trial step is then either accepted or rejected based on the some acceptable criteria which depends on reductions attained in the nonlinear objective function and in the measure of constraint infeasibility. Under the suitable assumptions, we prove that the algorithm is well defined and globally convergent. Finally, the preliminary numerical results are reported.

Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem

2010 ◽  
Vol 26 (4) ◽  
pp. 045003 ◽  
Author(s):  
Michael V Klibanov ◽  
Michael A Fiddy ◽  
Larisa Beilina ◽  
Natee Pantong ◽  
John Schenk
Keyword(s):  
Inverse Problem ◽  
Experimental Verification ◽  
Coefficient Inverse Problem ◽  
Globally Convergent ◽  
Convergent Algorithm

scholarly journals A globally convergent algorithm for MPCC

2015 ◽  
Vol 3 (3) ◽  
pp. 263-296 ◽  
Author(s):  
Abdeslam Kadrani ◽  
Jean Pierre Dussault ◽  
Abdelhamid Benchakroun
Keyword(s):  
Globally Convergent ◽  
Convergent Algorithm
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