scholarly journals Factorized quasi-Newton methods for nonlinear least squares problems

1991 ◽  
Vol 51 (1-3) ◽  
pp. 75-100 ◽  
Author(s):  
Hiroshi Yabe ◽  
Toshihiko Takahashi
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Newton Methods ◽  
Least Squares Problems ◽  
Quasi Newton

scholarly journals Stable factorized quasi-Newton methods for nonlinear least-squares problems

2001 ◽  
Vol 129 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
Ma Xiaofang ◽  
Fung Richard Ying Kit ◽  
Xu Chengxian
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Newton Methods ◽  
Least Squares Problems ◽  
Quasi Newton

Approximate Gauss–Newton methods for solving underdetermined nonlinear least squares problems

2017 ◽  
Vol 111 ◽  
pp. 92-110 ◽  
Author(s):  
Ji-Feng Bao ◽  
Chong Li ◽  
Wei-Ping Shen ◽  
Jen-Chih Yao ◽  
Sy-Ming Guu
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Newton Methods ◽  
Least Squares Problems

Approximate Gauss–Newton Methods for Nonlinear Least Squares Problems

2007 ◽  
Vol 18 (1) ◽  
pp. 106-132 ◽  
Author(s):  
S. Gratton ◽  
A. S. Lawless ◽  
N. K. Nichols
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Newton Methods ◽  
Least Squares Problems

scholarly journals A new limited memory method for unconstrained nonlinear least squares

2021 ◽  
Author(s):  
Morteza Kimiaei ◽  
Arnold Neumaier
Keyword(s):  
Least Squares ◽  
Jacobian Matrix ◽  
Trust Region ◽  
Nonlinear Least Squares ◽  
Black Box ◽  
Least Squares Problems ◽  
Trust Region Algorithm ◽  
Limited Memory ◽  
Adaptive Radius ◽  
Quasi Newton

AbstractThis paper suggests a new limited memory trust region algorithm for large unconstrained black box least squares problems, called LMLS. Main features of LMLS are a new non-monotone technique, a new adaptive radius strategy, a new Broyden-like algorithm based on the previous good points, and a heuristic estimation for the Jacobian matrix in a subspace with random basis indices. Our numerical results show that LMLS is robust and efficient, especially in comparison with solvers using traditional limited memory and standard quasi-Newton approximations.

scholarly journals A Superlinearly Convergent Penalty Method with Nonsmooth Line Search for Constrained Nonlinear Least Squares

2012 ◽  
Vol 16 ◽  
pp. 103 ◽  
Author(s):  
Nezam Mahdavi-Amiri ◽  
Mohammad Reza Ansari
Keyword(s):  
Least Squares ◽  
Penalty Method ◽  
Line Search ◽  
Search Strategy ◽  
Nonlinear Least Squares ◽  
Strategy Implementation ◽  
Test Problems ◽  
Least Squares Problems ◽  
Comparative Results ◽  
Quasi Newton

Recently, we have presented a projected structured algorithm for solving constrained nonlinear least squares problems, and established its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method. The structured adaptation also makes use of the ideas of Nocedal and Overton for handling the quasi-Newton updates of projected Hessians and appropriates the structuring scheme of Dennis, Martinez and Tapia. Here, for robustness, we present a specific nonsmooth line search strategy, taking account of the least squares objective. We also discuss the details of our new nonsmooth line search strategy, implementation details of the algorithm, and provide comparative results obtained by the testing of our program and three nonlinear programming codes from KNITRO on test problems (both small and large residuals) from Hock and Schittkowski, Lukšan and Vlček and some randomly generated ones due to Bartels and Mahdavi-Amiri. The results indeed affirm the practical relevance of our special considerations for the inherent structure of the least squares.    

scholarly journals Alternative structured spectral gradient algorithms for solving nonlinear least-squares problems

Heliyon ◽  
2021 ◽  
pp. e07499
Author(s):  
Mahmoud Muhammad Yahaya ◽  
Poom Kumam ◽  
Aliyu Muhammed Awwal ◽  
Sani Aji
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Least Squares Problems ◽  
Gradient Algorithms
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