Date:

Monday, April 14, 2008,
2:30 pm - 3:30 pm.

Place:

Mathematics Conference Room 626, UCD Building, 1250 14th St., Denver.

Speaker:

Dominique Orban.

Affiliation:

Mathematics and Industrial Engineering Department, École Polytechnique de Montréal, Québec, Canada.

Title:

Adaptive Interior-Point Methods for Nonlinear Programming.

Abstract:

We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and a line search, the decrease of the barrier parameter is automatically adjusted. We analyze global and local convergence properties, report numerical experiments on a standard collection of nonlinear problems and compare our results to a state-of-the-art interior-point implementation. In many instances, the adaptive algorithm reduces the number of iterations and of function evaluations. Its design guarantees a better fit between the magnitudes of the primal-dual residual and of the barrier parameter along the iterations.