Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems

2014 ◽  
Vol 8 ◽  
pp. 1247-1260
Author(s):  
Aliyu Usman Moyi ◽  
Mustafa Mamat ◽  
Wah June Leong
Keyword(s):  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Rank One ◽  
Symmetric Rank One

scholarly journals Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hong Seng Sim ◽  
Chuei Yee Chen ◽  
Wah June Leong ◽  
Jiao Li
Keyword(s):  
Unconstrained Optimization ◽  
Spectral Parameter ◽  
Gradient Method ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Rank One ◽  
Spectral Gradient Method ◽  
Symmetric Rank One ◽  
Large Scale Unconstrained Optimization

<p style='text-indent:20px;'>This paper proposes a nonmonotone spectral gradient method for solving large-scale unconstrained optimization problems. The spectral parameter is derived from the eigenvalues of an optimally sized memoryless symmetric rank-one matrix obtained under the measure defined as a ratio of the determinant of updating matrix over its largest eigenvalue. Coupled with a nonmonotone line search strategy where backtracking-type line search is applied selectively, the spectral parameter acts as a stepsize during iterations when no line search is performed and as a milder form of quasi-Newton update when backtracking line search is employed. Convergence properties of the proposed method are established for uniformly convex functions. Extensive numerical experiments are conducted and the results indicate that our proposed spectral gradient method outperforms some standard conjugate-gradient methods.</p>

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.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

1991 ◽  
Vol 2 (2-3) ◽  
pp. 175-182 ◽  
Author(s):  
D.T. Nguyen ◽  
O.O. Storaasli ◽  
E.A. Carmona ◽  
M. Al-Nasra ◽  
Y. Zhang ◽  
...  
Keyword(s):  
Structural Analysis ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Unconstrained Optimization Problems ◽  
Non Linear
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