Diagonal Approximation of the Hessian by Finite Differences for Unconstrained Optimization

2020 ◽  
Vol 185 (3) ◽  
pp. 859-879
Author(s):  
Neculai Andrei
Keyword(s):  
Unconstrained Optimization ◽  
Finite Differences ◽  
Diagonal Approximation

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.

THE METHOD OF FINITE DIFFERENCES APPLIED TO DESCRIPITION OF A METALIC COMPONENT

2017 ◽  
Author(s):  
Lisiane Trevisan ◽  
Juliane Donadel ◽  
Bianca de Castro
Keyword(s):  
Finite Differences

Finite differences with exponential filtering in the calculation of reactivity

Kerntechnik ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. 210-213 ◽  
Author(s):  
D. Suescún Díaz ◽  
A. Senra Martinez
Keyword(s):  
Finite Differences

Umbral Calculus

10.37236/24 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
A. Di Bucchianico ◽  
D. Loeb
Keyword(s):  
19Th Century ◽  
Finite Differences ◽  
State Of The Art ◽  
Umbral Calculus ◽  
Current State ◽  
Logical Foundation ◽  
Complete Bibliography ◽  
The 19Th Century ◽  
Mathematical Literature

We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 500 references) which we expect to update regularly.

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