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The Behavior of Newton-Type Methods on Two Equivalent Systems from Linear Programming
Newton-type methods are fundamental techniques for solving optimization problems. However, it is often not fully appreciated that these methods can produce significantly different behavior when applied to two equivalent ...
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 ...