### Sandra Pieraccini (University of Florence, Italy)

#### Inexact interior point methods for some classes of problems

*Wednesday 6 February 2002 at 16.30, JCMB 6309*

##### Abstract

Interior Point (IP) methods are very effective techniques for solving
several classes of optimization problems. IP methods are iterative methods
requiring at each iteration to solve a linear system in order to compute a
search direction. For large scale problems it is expensive to compute such
directions; moreover, it may be unnecessary to compute them with a high
accuracy if we are far from a solution. As a result it can be convenient to
use iterative methods for solving the linear system with an accuracy which
increases as far as we get closer to the solution. By using iterative methods
we obtain Inexact (or Truncated) IP methods.

We shall present an infeasible inexact path-following IP method for
solving the Nonlinear Complementarity Problem. The method compute inexactly
a search direction by performing an Inexact Newton step at each iteration.
Then, a suitable stepsize is searched in order to satisfy some classical
centering conditions and an Armijo rule for a given merit function.
Under proper assumptions fast global convergence is ensured.

We shall also propose possible application of Inexact Interior Point
methods so Semidefinite Programming, pointing out some open questions
concerning linear algebra issues.

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