Villalobos, CristinaTapia, RichardZhang, Yin2018-06-182018-06-181999-04Villalobos, Cristina, Tapia, Richard and Zhang, Yin. "The Sphere of Convergence of Newton's Method on Two Equivalent Systems from Nonlinear Programming." (1999) <a href="https://hdl.handle.net/1911/101920">https://hdl.handle.net/1911/101920</a>.https://hdl.handle.net/1911/101920We study a local feature of a Newton logarithmic barrier function method and a Newton primal-dual interior-point method. In particular, we study the radius of the sphere of convergence of Newton's method on two equivalent systems associated with the two aforementioned interior-point methods for nondegenerate problems in inequality contrained optimization problems. Our theoretical and numerical results are clearly in favor of using Newton primal-dual methods for solving the optimization problem. This work is an extension of the authors' earlier work [10] on linear programming problems.23 ppengTechnical reportTR99-15