New Class of Rank 1 Update for Solving Unconstrained Optimization Problem: New Class of Rank 1 Update for solving Unconstrained Optimization Problem

Saad Shakir  Mahmood; Jaafer Hmood  Eidi

doi:10.24996/ijs.2022.63.2.25

Authors

Saad Shakir Mahmood Mathematics Department, College of Education, Al-Mustansiriya University, Baghdad – Iraq
Jaafer Hmood Eidi Mathematics Department, College of Education, Al-Mustansiriya University, Baghdad – Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.2.25

Keywords:

Unconstrained optimization, Hessian matrix, modified Quasi-Newton condition, Positive definite

Abstract

The focus of this article is to add a new class of rank one of modified Quasi-Newton techniques to solve the problem of unconstrained optimization by updating the inverse Hessian matrix with an update of rank 1, where a diagonal matrix is the first component of the next inverse Hessian approximation, The inverse Hessian matrix is generated by the method proposed which is symmetric and it satisfies the condition of modified quasi-Newton, so the global convergence is retained. In addition, it is positive definite that guarantees the existence of the minimizer at every iteration of the objective function. We use the program MATLAB to solve an algorithm function to introduce the feasibility of the proposed procedure. Various numerical examples are given`.