Authors : Saad Shakir Mahmood and Jaafer Hmood Eidi
Abstract: 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.
Saad Shakir Mahmood and Jaafer Hmood Eidi, 2020. Modified BFGS Update Based on Determinant Property of Hessian Matrix. Journal of Modern Mathematics and Statistics, 14: 22-26.