A positional misalignment correction method for Fourier ptychographic microscopy based on the quasi-Newton method with a global optimization module

2019 ◽  
Vol 452 ◽  
pp. 296-305 ◽  
Author(s):  
Jinlei Zhang ◽  
Xiao Tao ◽  
Peng Sun ◽  
Zhenrong Zheng
Keyword(s):  
Global Optimization ◽  
Newton Method ◽  
Correction Method ◽  
Quasi Newton

scholarly journals A Perturbation Based Chaotic System Exploiting the Quasi-Newton Method for Global Optimization

2017 ◽  
Vol 27 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Keiji Tatsumi ◽  
Tetsuzo Tanino
Keyword(s):  
Global Optimization ◽  
Newton Method ◽  
Chaotic System ◽  
Local Minimum ◽  
Hessian Matrix ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Sufficient Condition ◽  
Parameter Values ◽  
Quasi Newton

The chaotic system has been exploited in metaheuristic methods of solving continuous global optimization problems. Recently, the gradient method with perturbation (GP) was proposed, which was derived from the steepest descent method for the problem with additional perturbation terms, and it was reported that chaotic metaheuristics with the GP have good performances of solving some benchmark problems. Moreover, the sufficient condition of its parameter values was theoretically shown under which its updating system is chaotic. However, the sufficient condition of its chaoticity and the width of strange attractor around each local minimum, which are important properties for exploiting the chaotic system in optimization, deeply depend on the eigenvalues of the Hessian matrix of the objective function at the local minimum. Thus, if the eigenvalues of different local minima are widely different from each other, or if it is different in different problems, such properties can cause the difficulty of selecting appropriate parameter values for an effective search. Therefore, in this paper, we propose modified GPs based on the quasi-Newton method instead of the steepest descent method, where their chaoticities and the width of strange attractor do not depend on the eigenvalue of the Hessian matrix at any local minimum due to the scale invariant of the quasi-Newton method. In addition, we empirically demonstrate that the parameter selection of the proposed methods is easier than the original GP, especially with respect to the step-size, and the chaotic metaheuristics with the proposed methods can find better solutions for some multimodal functions.

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

An improved constrained quasi-Newton method for the solution of inverse electromagnetic problems

1996 ◽  
Vol 32 (3) ◽  
pp. 1318-1321 ◽  
Author(s):  
C. Chat-Uthai ◽  
J.A. Ramirez ◽  
E.M. Freeman
Keyword(s):  
Newton Method ◽  
Electromagnetic Problems ◽  
Quasi Newton
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