TY  - JOUR
T1  - Modified BFGS Update Based on Determinant Property of Hessian Matrix
AU - Shakir Mahmood, Saad AU - Hmood Eidi, Jaafer 
JO  - Journal of Modern Mathematics and Statistics
VL  - 14
IS  - 2
SP  - 22
EP  - 26
PY  - 2020
DA  - 2001/08/19
SN  - 1994-5388
DO  - jmmstat.2020.22.26
UR  - https://makhillpublications.co/view-article.php?doi=jmmstat.2020.22.26
KW  - approximation
KW  -iteration
KW  -unconstrained optimization
KW  -Zhang-Xu condition
KW  -Quasi-Newton condition
KW  -minimizer
AB  - The aim of this study is to modified the BFGS
update based on the determinant property of Hessian
matrix by multiply the vector y (difference between the
next gradient and the current gradient) with a real number
say such that the determinant of the next Hessian matrix
equal to one at every iteration and because of the choice
of the initial Hessian approximation can be identity
matrix, so, the determinant of initial Hessian matrix is
also equal one and hence, the sequence of Hessian matrix
produced by the method never go to a near singular matrix
numerically which make the program never break before
get the minimizer of the objective function.
ER  -