Browsing by Author "Villalobos, Cristina"

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    The Behavior of Newton-Type Methods on Two Equivalent Systems from Linear Programming
    (1998-02) Villalobos, Cristina; Tapia, Richard; Zhang, Yin
    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 systems. In this paper, we investigate differences in local and global behavior of Newton-type methods when applied to the first-order optimality conditions for the logarithmic barrier formulation of the linear programming problem, and when applied to the perturbed first-order optimality conditions for the linear programming problem. Through theoretical analysis and numerical results, we show that Newton-type methods perform more effectively on the latter system than on the former system.
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    The Sphere of Convergence of Newton's Method on Two Equivalent Systems from Nonlinear Programming
    (1999-04) Villalobos, Cristina; Tapia, Richard; Zhang, Yin
    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 [10] on linear programming problems.