Optimization problems with complementarity constraints
A complementarity constraint requires that one of a pair of variables should be zero. Optimization problems with complementarity constraints are widespread, arising for example in transportation problems, energy optimization, and sparse optimization.
Rank minimization algorithms
We investigate the use of nonconvex approaches to rank minimization problems, an alternative to widely-used convex approaches such as nuclear norm minimization.
Modeling and Analysis of Wave Amplification in the Cochlea
The fundamental open question in understanding how we hear concerns the role of a nonlinear feedback mechanism known as the cochlear amplifier.
This project concerns developing theoretical models of processing taking place in a number of brain areas, mostly early sensory pathways. One set of problems we have addressed concerns the asynchronous steady state of a sparsely, randomly connected neuronal network. Another set of problems add
Research Training in Mathematical Modeling, Analysis and Computation
This is an interdisciplinary program for undergraduates, graduate students, and postdoctoral associates that integrates modeling, analysis, and computations with contemporary experimental research.
Advanced Computational Toolkit for Engineered Optical Materials (ACTEOM)
ACTEOM is a DARPA funded project, part of the EXTREME program, with the goal of developing an Advanced Computational Toolkit for Engineered Optical Materials (ACTEOM).
High-Order Accurate Partitioned Algorithms for Fluid-Structure Interactions and Conjugate-Heat Transfer
Fluid-structure interaction (FSI) problems are important in many areas of engineering and applied science such as modeling of blood flow, flow-induced vibrations of structures, and wave energy devices, and there is significant interest in numerical simulation tools for such problems. Conjugate h