A trust‐region method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils

2021 ◽  
Author(s):  
Jiao‐fen Li ◽  
Kai Wang ◽  
Yue‐yuan Liu ◽  
Xue‐feng Duan ◽  
Xue‐lin Zhou
Keyword(s):  
Eigenvalue Problem ◽  
Trust Region Method ◽  
Trust Region ◽  
Generalized Eigenvalue Problem ◽  
Region Method ◽  
Generalized Eigenvalue ◽  
Matrix Pencils

scholarly journals Solving the Trust-Region Subproblem By a Generalized Eigenvalue Problem

2017 ◽  
Vol 27 (1) ◽  
pp. 269-291 ◽  
Author(s):  
Satoru Adachi ◽  
Satoru Iwata ◽  
Yuji Nakatsukasa ◽  
Akiko Takeda
Keyword(s):  
Eigenvalue Problem ◽  
Trust Region ◽  
Generalized Eigenvalue Problem ◽  
Trust Region Subproblem ◽  
Generalized Eigenvalue

Newton’s method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils

2021 ◽  
Vol 47 (2) ◽  
Author(s):  
Jiao-fen Li ◽  
Wen Li ◽  
Xue-feng Duan ◽  
Mingqing Xiao
Keyword(s):  
Eigenvalue Problem ◽  
Newton’S Method ◽  
Newton's Method ◽  
Generalized Eigenvalue Problem ◽  
Generalized Eigenvalue ◽  
Matrix Pencils

A Riemannian Optimization Approach for Solving the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils

2020 ◽  
Vol 82 (3) ◽  
Author(s):  
Jiao-fen Li ◽  
Wen Li ◽  
Seak-Weng Vong ◽  
Qi-Lun Luo ◽  
MingQing Xiao
Keyword(s):  
Eigenvalue Problem ◽  
Generalized Eigenvalue Problem ◽  
Optimization Approach ◽  
Riemannian Optimization ◽  
Generalized Eigenvalue ◽  
Matrix Pencils

Based on GA Mixed with Trust Region Method Solving Nonlinear Least Square Problems

2011 ◽  
Vol 141 ◽  
pp. 92-97
Author(s):  
Miao Hu ◽  
Tai Yong Wang ◽  
Bo Geng ◽  
Qi Chen Wang ◽  
Dian Peng Li
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Least Square ◽  
Search Range ◽  
Genetic Search ◽  
Region Method ◽  
Unconstrained Optimization Problems ◽  
Least Square Problems

Nonlinear least square is one of the unconstrained optimization problems. In order to solve the least square trust region sub-problem, a genetic algorithm (GA) of global convergence was applied, and the premature convergence of genetic algorithms was also overcome through optimizing the search range of GA with trust region method (TRM), and the convergence rate of genetic algorithm was increased by the randomness of the genetic search. Finally, an example of banana function was established to verify the GA, and the results show the practicability and precision of this algorithm.

A BFGS trust-region method for nonlinear equations

Computing ◽  
2011 ◽  
Vol 92 (4) ◽  
pp. 317-333 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei ◽  
Xiwen Lu
Keyword(s):  
Nonlinear Equations ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method
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