Global convergence of the non-quasi-newton method for unconstrained optimization problems

2006 ◽  
Vol 21 (3) ◽  
pp. 276-288
Author(s):  
Liu Hongwei ◽  
Wang Mingjie ◽  
Li Jinshan ◽  
Zhang Xiangsun
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Quasi Newton

scholarly journals A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2093
Author(s):  
Huiping Cao ◽  
Xiaomin An
Keyword(s):  
Unconstrained Optimization ◽  
Newton Method ◽  
Automatic Differentiation ◽  
Optimization Problems ◽  
Symmetric Matrix ◽  
Matrix Completion ◽  
Bfgs Method ◽  
Limited Memory ◽  
Unconstrained Optimization Problems ◽  
Quasi Newton

In our paper, we introduce a sparse and symmetric matrix completion quasi-Newton model using automatic differentiation, for solving unconstrained optimization problems where the sparse structure of the Hessian is available. The proposed method is a kind of matrix completion quasi-Newton method and has some nice properties. Moreover, the presented method keeps the sparsity of the Hessian exactly and satisfies the quasi-Newton equation approximately. Under the usual assumptions, local and superlinear convergence are established. We tested the performance of the method, showing that the new method is effective and superior to matrix completion quasi-Newton updating with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method and the limited-memory BFGS method.

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
Author(s):  
Ping Hu ◽  
Zong-yao Wang
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Combination ◽  
Combination Rule ◽  
Combination Technique ◽  
Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

scholarly journals Global Convergence of a Modified Two-Parameter Scaled BFGS Method with Yuan-Wei-Lu Line Search for Unconstrained Optimization

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Pengyuan Li ◽  
Zhan Wang ◽  
Dan Luo ◽  
Hongtruong Pham
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Medium Size ◽  
Bfgs Method ◽  
Nonconvex Functions ◽  
Bfgs Update ◽  
Unconstrained Optimization Problems ◽  
Quasi Newton ◽  
Two Parameter

The BFGS method is one of the most efficient quasi-Newton methods for solving small- and medium-size unconstrained optimization problems. For the sake of exploring its more interesting properties, a modified two-parameter scaled BFGS method is stated in this paper. The intention of the modified scaled BFGS method is to improve the eigenvalues structure of the BFGS update. In this method, the first two terms and the last term of the standard BFGS update formula are scaled with two different positive parameters, and the new value of yk is given. Meanwhile, Yuan-Wei-Lu line search is also proposed. Under the mentioned line search, the modified two-parameter scaled BFGS method is globally convergent for nonconvex functions. The extensive numerical experiments show that this form of the scaled BFGS method outperforms the standard BFGS method or some similar scaled methods.

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