Modified BFGS Update (H-Version) Based on the Determinant Property of Inverse of Hessian Matrix for Unconstrained Optimization

Main Article Content

Saad Shakir Mahmood
https://orcid.org/0000-0001-5433-9710

Abstract

The study presents the modification of the Broyden-Flecher-Goldfarb-Shanno (BFGS) update (H-Version) based on the determinant property of inverse of Hessian matrix (second derivative of the objective function), via updating of the vector s ( the difference between the next solution and the current solution), such that the determinant of the next inverse of Hessian matrix is equal to the determinant of the current inverse of Hessian matrix at every iteration. Moreover, the sequence of inverse of Hessian matrix generated by the method would never  approach a near-singular matrix, such that the program would never break before the minimum value of the objective function is obtained. Moreover, the new modification of BFGS update (H-version) preserves the symmetric property and the positive definite property without any condition.

Downloads

Download data is not yet available.

Article Details

How to Cite
1.
Mahmood S. Modified BFGS Update (H-Version) Based on the Determinant Property of Inverse of Hessian Matrix for Unconstrained Optimization. BSJ [Internet]. 8Sep.2020 [cited 26Sep.2020];17(3(Suppl.):0994. Available from: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/3672
Section
article