A new method of moving asymptotes for large-scale unconstrained optimization

2008 ◽  
Vol 203 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Haijun Wang ◽  
Qin Ni
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
New Method ◽  
Method Of Moving Asymptotes ◽  
Large Scale Unconstrained Optimization ◽  
Moving Asymptotes

A CONVEX APPROXIMATION METHOD FOR LARGE SCALE LINEAR INEQUALITY CONSTRAINED MINIMIZATION

2010 ◽  
Vol 27 (01) ◽  
pp. 85-101
Author(s):  
HAI-JUN WANG ◽  
QIN NI
Keyword(s):  
Large Scale ◽  
Linear Inequality ◽  
Trust Region ◽  
Inequality Constraints ◽  
New Method ◽  
Approximation Properties ◽  
Linear Inequality Constraints ◽  
Method Of Moving Asymptotes ◽  
Large Scale Problems ◽  
Moving Asymptotes

A new method of moving asymptotes for large scale minimization subject to linear inequality constraints is discussed in this paper. In each step of the iterative process, a descend direction is obtained by solving a convex separable subproblem with dual technique. The new rules for controlling the asymptotes parameters are designed by the trust region radius and some approximation properties such that the global convergence of the new method are obtained. The numerical results show that the new method may be capable of processing some large scale problems.

scholarly journals A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 227
Author(s):  
Zabidin Salleh ◽  
Ghaliah Alhamzi ◽  
Ibitsam Masmali ◽  
Ahmad Alhawarat
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Numerical Results ◽  
New Method ◽  
Unconstrained Optimization Problems ◽  
Large Scale Unconstrained Optimization

The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require the second derivative, such as Newton’s method or approximations. Moreover, the conjugate gradient method can be applied in many fields such as neural networks, image restoration, etc. Many complicated methods are proposed to solve these optimization functions in two or three terms. In this paper, we propose a simple, easy, efficient, and robust conjugate gradient method. The new method is constructed based on the Liu and Storey method to overcome the convergence problem and descent property. The new modified method satisfies the convergence properties and the sufficient descent condition under some assumptions. The numerical results show that the new method outperforms famous CG methods such as CG-Descent5.3, Liu and Storey, and Dai and Liao. The numerical results include the number of iterations and CPU time.

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