The Sphere of Convergence of Newton's Method
on Two Equivalent Systems from Linear and Nonlinear Programming
Cristina Villalobos
Department of Mathematics, University of TexasPan American
Wednesday, April 23, 2003 14:0015:00, Room 145, NIST North (820) Gaithersburg Wednesday, April 23, 2003 12:0013:00, Room 4550 Boulder
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 logbarrier function formulation and the perturbed optimality
conditions. Primal and primaldual interiorpoint 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.
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at least 24 hours in advance.
