scholarly journals An Alternative Approach for Finding Newton's Direction in Solving Large-Scale Unconstrained Optimization for Problems with an Arrowhead Hessian Matrix

2020 ◽  
Vol 8 (2A) ◽  
pp. 40-46
Author(s):  
Khadizah Ghazali ◽  
Jumat Sulaiman ◽  
Yosza Dasril ◽  
Darmesah Gabda
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Hessian Matrix ◽  
Alternative Approach ◽  
Large Scale Unconstrained Optimization

scholarly journals Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Mahboubeh Farid ◽  
Wah June Leong ◽  
Najmeh Malekmohammadi ◽  
Mustafa Mamat
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Hessian Matrix ◽  
Main Idea ◽  
Numerical Comparison ◽  
Rapid Control ◽  
Diagonal Approximation ◽  
Gradient Type ◽  
Diagonal Updating ◽  
Large Scale Unconstrained Optimization

We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant.

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