Open AccessNew Class of Rank 1 Update for Solving Unconstrained Optimization Problem
Author(s) -
Saad Shakir Mahmood,
Jaafer Hmood Eidi
Publication year - 2022
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2022.63.2.25
Subject(s) - hessian matrix , quasi newton method , rank (graph theory) , mathematics , convergence (economics) , mathematical optimization , diagonal matrix , diagonal , inverse , matrix (chemical analysis) , class (philosophy) , function (biology) , focus (optics) , positive definite matrix , newton's method , computer science , combinatorics , nonlinear system , eigenvalues and eigenvectors , artificial intelligence , materials science , economic growth , optics , composite material , biology , geometry , quantum mechanics , evolutionary biology , physics , economics
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`.