Research
Mixed-Integer Nonlinear Programming
Nonconvex objectives and inequalities are notoriously difficult to deal with, both from a theoretical and practical perspective. These issues become amplified when we further request that solutions are integer. How can we improve our understanding of these difficult problems and also improve our ability to solve them?
Cutting Plane Theory and Practice
Cutting planes allow us to add inequalities that are valid for the integer points, but cut off portions of the LP relaxation and bring us closer to the integer hull. These cuts are a fundamental tool used in efficiently solving integer programs. Although we have made significant progress in recent years, it is still unclear what the maximum potential of cutting planes is and how to properly utilize a variety of possible cuts.
Redistricting
The 2020 census data is almost upon us. After which, all states in the will develop new district plans. But how do we ensure that we create fair, quality plans that are free of gerrymandering?
Autonomous Scheduling and Robotic Motion
With the advancement of robotics, this bring about many complicated problems to solve. How should a fleet of machines work together to accomplish tasks? Furthermore, how can we plan for these machines to work together in the presence of many uncertainties with time it takes to complete jobs or even whether a machine will be successful at completing a job. This becomes a very difficult stochastic scheduling problem that needs requires efficient quality solutions with guarantees. This work is done in conjunction with Dr. Komendera, the director of the Field and Space Robotics Laboratory.
