ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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The Sphere of Convergence of Newton's Method on Two Equivalent Systems from Linear and Nonlinear Programming

Cristina Villalobos
Department of Mathematics, University of Texas-Pan American

Wednesday, April 23, 2003 14:00-15:00,
Room 145, NIST North (820)
Wednesday, April 23, 2003 12:00-13:00,
Room 4550

Abstract: Newton's method is a fundamental technique underlying many numerical methods for solving systems of nonlinear equations and optimization problems. However, it is often not fully appreciated that Newton's method can produce significantly different behavior when applied to equivalent systems, i.e., problems with the same solution but different mathematical formulations. We study a local feature of Newton's method applied to two equivalent systems from linear and nonlinear programming: the optimality conditions of the log-barrier function formulation and the perturbed optimality conditions. Primal and primal-dual interior-point methods for linear and nonlinear programs are comprised of these two systems. In particular, we provide an asymptotic analysis on the radius of the sphere of convergence of Newton's method on the two equivalent systems for nondegenerate linear and nonlinear programs. We show that the radii are different for each system.
Contact: A. J. Kearsley

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