The Sphere of Convergence of Newton's Method on Two Equivalent Systems from Nonlinear Programming
We 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  on linear programming problems.
Citable link to this pagehttps://hdl.handle.net/1911/101920
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