THE NEW RANK ONE CLASS FOR UNCONSTRAINED PROBLEMS SOLVING - Mustafa, Ahmed (Science Journal of University of Zakho, 2023)
One of the most well-known methods for unconstrained problems is the quasi-Newton approach, iterative solutions. The great precision and quick convergence of the quasi-Newton methods are well recognized. In this work, the new algorithm for the symmetric rank one SR1 method is driven.The strong Wolfe line search criteria deﬁne the step length selection. We also proved the new quasi-Newton equation and positive definite matrix theorem. Preliminary computer testing on the set of fourteen unrestricted optimization test functions leads to the conclusion that this new method is more effective and durable than the implementation of classical SR1 method in terms of iterations count and functions.
Keywords: Quasi-Newton; Symmetric Rank One; Positive Definite Matrix; Unconstrained Optimization; Nonlinear Optimization