Nonlinear conjugate gradient method for designing diffractive optical elements focusing desired optical intensity distributions on arbitrarily curved surfaces

2006 ◽  
Author(s):  
Hwi Kim ◽  
Byoungho Lee
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Curved Surfaces ◽  
Optical Intensity ◽  
Diffractive Optical Elements ◽  
Optical Elements ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient

scholarly journals A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shengwei Yao ◽  
Xiwen Lu ◽  
Bin Qin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Special Role ◽  
Conjugacy Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
The Given

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. In this paper, we propose a new conjugacy condition which is similar to Dai-Liao (2001). Based on this condition, the related nonlinear conjugate gradient method is given. With some mild conditions, the given method is globally convergent under the strong Wolfe-Powell line search for general functions. The numerical experiments show that the proposed method is very robust and efficient.

scholarly journals A new three-term conjugate gradient method for solving the finite minimax problems

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 737-758
Author(s):  
Yue Hao ◽  
Shouqiang Du ◽  
Yuanyuan Chen
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problem ◽  
Minimax Problems ◽  
Minimax Problem ◽  
Constrained Optimization Problem ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
Finite Minimax

In this paper, we consider the method for solving the finite minimax problems. By using the exponential penalty function to smooth the finite minimax problems, a new three-term nonlinear conjugate gradient method is proposed for solving the finite minimax problems, which generates sufficient descent direction at each iteration. Under standard assumptions, the global convergence of the proposed new three-term nonlinear conjugate gradient method with Armijo-type line search is established. Numerical results are given to illustrate that the proposed method can efficiently solve several kinds of optimization problems, including the finite minimax problem, the finite minimax problem with tensor structure, the constrained optimization problem and the constrained optimization problem with tensor structure.

Sign in / Sign up

Export Citation Format

Share Document