The Mathematical Institute, University of Oxford, Eprints Archive

A new perspective on the complexity of interior point methods for linear programming

Cartis, Coralia and Hauser, Raphael (2007) A new perspective on the complexity of interior point methods for linear programming. Technical Report. Unspecified. (Submitted)

[img]
Preview
PDF
258Kb

Abstract

In a dynamical systems paradigm, many optimization algorithms are equivalent to applying forward Euler method to the system of ordinary differential equations defined by the vector field of the search directions. Thus the stiffness of such vector fields will play an essential role in the complexity of these methods. We first exemplify this point with a theoretical result for general linesearch methods for unconstrained optimization, which we further employ to investigating the complexity of a primal short-step path-following interior point method for linear programming. Our analysis involves showing that the Newton vector field associated to the primal logarithmic barrier is nonstiff in a sufficiently small and shrinking neighbourhood of its minimizer. Thus, by confining the iterates to these neighbourhoods of the primal central path, our algorithm has a nonstiff vector field of search directions, and we can give a worst-case bound on its iteration complexity. Furthermore, due to the generality of our vector field setting, we can perform a similar (global) iteration complexity analysis when the Newton direction of the interior point method is computed only approximately, using some direct method for solving linear systems of equations.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1097
Deposited By:Lotti Ekert
Deposited On:07 May 2011 09:02
Last Modified:07 May 2011 09:02

Repository Staff Only: item control page