Limited memory quasi-newton method for large-scale linearly equality-constrained minimization

2000 ◽  
Vol 16 (3) ◽  
pp. 320-328 ◽  
Author(s):  
Ni Qin
Keyword(s):  
Newton Method ◽  
Large Scale ◽  
Constrained Minimization ◽  
Limited Memory ◽  
Quasi Newton

scholarly journals A Stochastic Quasi-Newton Method for Large-Scale Nonconvex Optimization With Applications

2020 ◽  
Vol 31 (11) ◽  
pp. 4776-4790 ◽  
Author(s):  
Huiming Chen ◽  
Ho-Chun Wu ◽  
Shing-Chow Chan ◽  
Wong-Hing Lam
Keyword(s):  
Newton Method ◽  
Nonconvex Optimization ◽  
Large Scale ◽  
Quasi Newton

scholarly journals A Newton-Like Trust Region Method for Large-Scale Unconstrained Nonconvex Minimization

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Weiwei ◽  
Yang Yueting ◽  
Zhang Chenhui ◽  
Cao Mingyuan
Keyword(s):  
Large Scale ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Nonconvex Minimization ◽  
Trust Region Subproblem ◽  
Newton Equation ◽  
Limited Memory ◽  
Quasi Newton ◽  
Approximate Hessian

We present a new Newton-like method for large-scale unconstrained nonconvex minimization. And a new straightforward limited memory quasi-Newton updating based on the modified quasi-Newton equation is deduced to construct the trust region subproblem, in which the information of both the function value and gradient is used to construct approximate Hessian. The global convergence of the algorithm is proved. Numerical results indicate that the proposed method is competitive and efficient on some classical large-scale nonconvex test problems.

scholarly journals A Stochastic Quasi-Newton Method for Large-Scale Optimization

2016 ◽  
Vol 26 (2) ◽  
pp. 1008-1031 ◽  
Author(s):  
R. H. Byrd ◽  
S. L. Hansen ◽  
Jorge Nocedal ◽  
Y. Singer
Keyword(s):  
Newton Method ◽  
Large Scale ◽  
Large Scale Optimization ◽  
Scale Optimization ◽  
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.

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