Harbir Antil - Research

Multilevel Methods in PDE Constrained Optimization

For a description of PDE constrained optimization problems we refer to: link

Goal

The aim of this project is to develop, analyze and implement a class of optimization algorithms that integrate multilevel iterative solvers and so-called all-at-once optimization methods.

Collaborators

Jiwen He (University of Houston)
Matthias Heinkenschloss (Rice University)
Ronald H. W. Hoppe (University of Houston)
Christopher Linsenmann (University of Augsburg)

Achievements

We consider the shape optimization problems with PDE constraints. For practical purposes design variables the state and control constraints are taken into account as well.

We have developed an adaptive multilevel interior-point method of barrier type featuring a predictor-corrector continuation method with an adaptive choice of the barrier parameter along the barrier path.

Relevant Publications

H. Antil, R. H.W. Hoppe, and C. Linsenmann.
Optimal design of stationary flow problems by path-following interior-point.
Control and Cybernetics (2008) 37(4):771-796. preprint

H. Antil, R. H.W. Hoppe, and C. Linsenmann.
Path-following primal-dual interior-point methods for shape optimization of stationary flow problems.
Journal of Numerical Mathematics (2007) 15(2):81-100. preprint

H. Antil, R. H.W. Hoppe, and C. Linsenmann.
Adaptive Multilevel Interior Point Methods in PDE Constrained Optimization.
Proc. Int. Conf. on Domain Decomposition Methods and Applications XVIII (M. Bercovier et al.; eds.), Lecture Notes in Computer Science and Engineering (2009), 70:15-26, Springer, Berlin-Heidelberg-New York.

H. Antil, R. H.W. Hoppe, and C. Linsenmann.
Adaptive Path-following Primal-Dual Interior Point Methods for Shape Optimization of Linear and Nonlinear Stokes Flow Problems.
Lecture Notes in Computer Science (2008), 4818:259-266, Springer, Berlin-Heidelberg-New York.