Quasi-Newton trust region algorithm for non-smooth least squares problems

1999 ◽  
Vol 105 (2-3) ◽  
pp. 183-194 ◽  
Author(s):  
W. Sun ◽  
R.J.B. Sampaio ◽  
J. Yuan
Keyword(s):  
Least Squares ◽  
Trust Region ◽  
Least Squares Problems ◽  
Trust Region Algorithm ◽  
Quasi Newton

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 An adaptive trust region algorithm for large-residual nonsmooth least squares problems

2018 ◽  
Vol 14 (2) ◽  
pp. 707-718
Author(s):  
Zhou Sheng ◽  
◽  
Gonglin Yuan ◽  
Zengru Cui ◽  
Xiabin Duan ◽  
...  
Keyword(s):  
Least Squares ◽  
Trust Region ◽  
Least Squares Problems ◽  
Trust Region Algorithm

scholarly journals A Filter and Nonmonotone Adaptive Trust Region Line Search Method for Unconstrained Optimization

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 656
Author(s):  
Quan Qu ◽  
Xianfeng Ding ◽  
Xinyi Wang
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Hessian Matrix ◽  
Trust Region ◽  
Approximate Model ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Line Search Method ◽  
Quasi Newton

In this paper, a new nonmonotone adaptive trust region algorithm is proposed for unconstrained optimization by combining a multidimensional filter and the Goldstein-type line search technique. A modified trust region ratio is presented which results in more reasonable consistency between the accurate model and the approximate model. When a trial step is rejected, we use a multidimensional filter to increase the likelihood that the trial step is accepted. If the trial step is still not successful with the filter, a nonmonotone Goldstein-type line search is used in the direction of the rejected trial step. The approximation of the Hessian matrix is updated by the modified Quasi-Newton formula (CBFGS). Under appropriate conditions, the proposed algorithm is globally convergent and superlinearly convergent. The new algorithm shows better performance in terms of the Dolan–Moré performance profile. Numerical results demonstrate the efficiency and robustness of the proposed algorithm for solving unconstrained optimization problems.

scholarly journals Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-17
Author(s):  
Mohammedi R. Abdel-Aziz ◽  
Mahmoud M. El-Alem
Keyword(s):  
Least Squares ◽  
Original Problem ◽  
Krylov Subspace ◽  
Quadratic Function ◽  
Trust Region ◽  
Nonlinear Least Squares ◽  
Dimensional Subspace ◽  
Convergence Theory ◽  
Least Squares Problems ◽  
Programming Algorithms

The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm is based on constructing a basis for the Krylov subspace in conjunction with a model trust region technique to choose the step. The computational step on the small dimensional subspace lies inside the trust region. The Krylov subspace is terminated such that the termination condition allows the gradient to be decreased on it. A convergence theory of this algorithm is presented. It is shown that this algorithm is globally convergent.

A smoothing trust region filter algorithm for nonsmooth least squares problems

2016 ◽  
Vol 59 (5) ◽  
pp. 999-1014 ◽  
Author(s):  
XiaoJun Chen ◽  
ShouQiang Du ◽  
Yang Zhou
Keyword(s):  
Least Squares ◽  
Trust Region ◽  
Least Squares Problems
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