A restarting approach for the symmetric rank one update for unconstrained optimization

2007 ◽  
Vol 42 (3) ◽  
pp. 327-334 ◽  
Author(s):  
Wah June Leong ◽  
Malik Abu Hassan
Keyword(s):  
Unconstrained Optimization ◽  
Rank One ◽  
Symmetric Rank One

scholarly journals Structured symmetric rank-one method for unconstrained optimization

2011 ◽  
Vol 88 (12) ◽  
pp. 2608-2617 ◽  
Author(s):  
Farzin Modarres ◽  
Malik Abu Hassan ◽  
Wah June Leong
Keyword(s):  
Unconstrained Optimization ◽  
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>

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