scholarly journals Scaled memoryless BFGS preconditioned steepest descent method for very large-scale unconstrained optimization

2009 ◽  
Vol 30 (2) ◽  
pp. 387-396 ◽  
Author(s):  
Wah June Leong ◽  
Malik Abu Hassan
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Large Scale Unconstrained Optimization

scholarly journals A modification of steepest descent method for solving large-scaled unconstrained optimization problems

2018 ◽  
Vol 7 (3.28) ◽  
pp. 72
Author(s):  
Siti Farhana Husin ◽  
Mustafa Mamat ◽  
Mohd Asrul Hery Ibrahim ◽  
Mohd Rivaie
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Search Direction ◽  
Exact Line Search ◽  
Scale Optimization

In this paper, we develop a new search direction for Steepest Descent (SD) method by replacing previous search direction from Conjugate Gradient (CG) method, , with gradient from the previous step,  for solving large-scale optimization problem. We also used one of the conjugate coefficient as a coefficient for matrix . Under some reasonable assumptions, we prove that the proposed method with exact line search satisfies descent property and possesses the globally convergent. Further, the numerical results on some unconstrained optimization problem show that the proposed algorithm is promising. 

scholarly journals A Simple Sufficient Descent Method for Unconstrained Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Ming-Liang Zhang ◽  
Yun-Hai Xiao ◽  
Dangzhen Zhou
Keyword(s):  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
Unconstrained Minimization ◽  
Descent Method ◽  
Minimization Problems ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

We develop a sufficient descent method for solving large-scale unconstrained optimization problems. At each iteration, the search direction is a linear combination of the gradient at the current and the previous steps. An attractive property of this method is that the generated directions are always descent. Under some appropriate conditions, we show that the proposed method converges globally. Numerical experiments on some unconstrained minimization problems from CUTEr library are reported, which illustrate that the proposed method is promising.

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