Professor Mitchell's interests are in various areas of optimization. From a theoretical point of view, he develops algorithms for integer optimization, conic optimization problems, and problems with complementarity constraints, areas that have multiple applications in allocation of resources as well as in other areas of science. One particular current area is in sparse and low-rank optimization, especially in the use of exact complementarity formulations. Sparse formulations occur in, for example, compressed sensing and genome-wide association studies. Low-rank optimization is also used in some problems in compressed sensing and also in statistics and in financial optimization. Current application areas of particular interest are in effective resource allocation in disaster management and humanitarian logistics, looking both at preparation and mitigation for a potential disaster, and in recovery from a disaster. He also looks at the related area of designing resilient supply chains.