Optimization principles can be applied to several problems and areas. In fact, optimization is used every day — from TV shows that target advertisements to specific population segments to a radiologist that uses selective beam radiation that targets cancer cells in a lung cancer patient.
Many of these problems can be formulated as one of the standard paradigms in optimization, including linear programming, network optimization, nonlinear programming, stochastic optimization, or complementarity or variational inequality. In their research, optimization specialists develop algorithms for these and other types of optimization problems, study their mathematical properties and practical performance to implement them in high-quality software and apply them to practical problems.
Consider a project involving packing ellipsoids of given (but varying) dimensions into a finite container in a way that minimizes the maximum overlap between adjacent ellipsoids. A bilevel optimization algorithm is described for finding local solutions, for both the general case and the easier special case in which the ellipsoids are spheres. Algorithm and […]
Operational (tactical) and strategic mathematical models are used in the optimization decision process to determine more efficient and effective ways to control and manage a system or process. Mathematical models are routinely used in natural sciences (physics, biology), engineering (artificial intelligence, computer science) and social science (economics, political science). However, the lack of agreement between […]
Large data sets require statistical analysis, but some data may come in varied forms (text, audio, video, sensor data, etc.). To cope with data structure variations, optimization explores integrating statistical processing techniques with data processing systems to make such systems easer to build, maintain and deploy. Mass digitization of printed media into plain test is changing […]
Research projects determine the optimum electrical power flow or examines reconfiguring power systems. Since changes in energy generation, storage and flow has regional and national implications, most projects involve extensive collaboration with state and/or federal agencies.
Dedicated to examining the application of simulation and optimization techniques to address questions about ecology, conservation, and natural resource management.
Our research on radiotherapy for cancer treatments optimizes a narrow X-ray beam radiation dose that targets tumors while minimizing radiation exposure in surrounding healthy tissue.