Interior point methods are the state of the art algorithms for solving optimization problems. Following Rice University's tradition in optimization theory, Yin Zhang designs interior point methods for special optimization problems. Matthias Heinkenschloss studies how interior point methods behave in the presence of uncertainty on the parameters.
Highlights
Medical applications research thrives in the department, with extensive collaboration with other departments at Rice and prestigious medical institutions, such as the MD Anderson Center.
Learn more about the exciting research done at CAAM to fight cancer with Intensity Modulated Radiation Therapy and Medical Image Registration.
The constraints on an optimization problem, such as one involving fluid flow, often involve the solution of partial differential equations. Researchers at CAAM have an intense interest in the numerical solution of large-scale nonlinear optimization problems that have these types of constraints.
One of the research topics of CAAM student Denis Ridzal, supervised by Matthias Heinkenschloss, is to find a way to control the temperature on the boundary of a fluid flow adjacent to a solid, in order to achieve a given temperature inside the solid. An answer to this problem is important, for instance, in industrial applications that need to cool metals.
Perhaps we could make a nice subpage with more info about this and the work done by other students. Also, I think we can get more attractive graphics.
Real life optimization problems are not always specified as mathematicians would like them to be. The quantities that one wishes to optimize often carry errors or uncertainty. Robust optimization deals with the solution of optimization problems with uncertainty in the parameters.
For instance, in a problem involving the construction of a building, we may be interested in the stability of the building subject to a wide variety of unknown combinations of forces. Also, in some applications it is crucial to study how the error committed by discretizing the optimization problem carries over to the solution. This topic is among the research interests of Yin Zhang, Matthias Heinkenschloss and students Denis Ridzal and Dwayne Williams.
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| Matthias Heinkenschloss | Richard A. Tapia | Yin Zhang |
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| Robert E. Bixby | John E. Dennis, Jr | |
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