Operations Research
The Operations Research area has three themes of primary focus: computational geometry, quantitative finance and stochastic optimization. The computational geometry group consists of Esther Arkin and Joe Mitchell along with adjunct faculty Michael Bender, Jie Gao, and Steve Skiena in Computer Science. The quantitative finance group consists of Robert Frey, a former Managing Director at Renaissance Technologies, and Haipeng Xing. The stochastic optimization group consists of Eugene Feinberg and Haipeng Hu, along with adjunct professor Hussein Badr in Computer Science.
Computational Geometry
Esther Arkin's primary research area is the design and analysis of algorithms that arise in network optimization, computational geometry, graph theory, scheduling, robotics, geographic information systems, computer graphics, manufacturing, and computer vision. Arkin is interested in theoretical analysis of worst-case complexity of problems, especially those that require optimization. She collaborates extensively with Joe Mitchell. For more information, see Arkin webpage.
Joe Mitchell's primary research area is computational geometry, applied to pratical problems in computer graphics, visualization, robotics, manufacturing, geographic information systems, and computer vision. Mitchell is one of the country's leaders in computational geometry, which studies the design, analysis, and implementation of efficient algorithms to solve geometric problems; in the 1990's, he chaired the National Science Foundation advisory committee in computational geometry. A major current application is helping air traffic controllers route airplanes around storm systems as they approach an airport. For more information, see Mitchell webpage.
Quantitative Finance
Robert Frey had worked in an array of operations research related managerial positions before earning his PhD as a part-time student in 1986. Then he became involved in designing mathematically based financial trading systems, first at Morgan Stanley, then at Kepler Associates, and finally at Renaissance Technologies, from which he retired at the rank of Managing Director in 2004. He and his students are investigating a number of problems where current mathematical models do not describe market behavior well. Among his many investment and advisory roles, he chairs the advisory committee of the U. of Chicago Financial Mathematics program (the countryÕs top ranked quantitative finance program). For more information, see Frey webpage.
Haipeng Xing is a statistician whose research is focused on statistical problem in quantitative, in particular (i) change-points detection, parameter estimation and adaptive control problems and their applications in engineering, economics and genetics; (ii) statistical models and methods in financial econometrics and engineering; and (iii) time series modeling. He is co-author, with T.L. Lai of Stanford, of a widely used textbook on statistical methods in finance. For more information, see Xing webpage.
Stochastic Optimization
Eugene Feinberg works in stochastic methods of operations research and their industrial applications. He is one of the leaders in Markov decision processes and its application to telecommunication, manufacturing, transportation, service and to other man-made systems. He is also one of the country's experts on optimizing electric energy transmission and forecasting energy demand. For more information, see Feinberg webpage.
Jiaqiao Hu's research is focused on designing and analyzing randomized algorithms for solving Markov decision processes and global optimization problems. He has been investigating new sampling and simulation-based techniques to overcome the computational difficulties associated with traditional methods, where sampling and simulation techniques are used not only to avoid enumerating the entire solution space but also to resolve the issue of the unavailability of explicit mathematical models of the underlying systems. For more information, see Hu webpage.
Computational Geometry
Esther Arkin's primary research area is the design and analysis of algorithms that arise in network optimization, computational geometry, graph theory, scheduling, robotics, geographic information systems, computer graphics, manufacturing, and computer vision. Arkin is interested in theoretical analysis of worst-case complexity of problems, especially those that require optimization. She collaborates extensively with Joe Mitchell. For more information, see Arkin webpage.
Joe Mitchell's primary research area is computational geometry, applied to pratical problems in computer graphics, visualization, robotics, manufacturing, geographic information systems, and computer vision. Mitchell is one of the country's leaders in computational geometry, which studies the design, analysis, and implementation of efficient algorithms to solve geometric problems; in the 1990's, he chaired the National Science Foundation advisory committee in computational geometry. A major current application is helping air traffic controllers route airplanes around storm systems as they approach an airport. For more information, see Mitchell webpage.
Quantitative Finance
Robert Frey had worked in an array of operations research related managerial positions before earning his PhD as a part-time student in 1986. Then he became involved in designing mathematically based financial trading systems, first at Morgan Stanley, then at Kepler Associates, and finally at Renaissance Technologies, from which he retired at the rank of Managing Director in 2004. He and his students are investigating a number of problems where current mathematical models do not describe market behavior well. Among his many investment and advisory roles, he chairs the advisory committee of the U. of Chicago Financial Mathematics program (the countryÕs top ranked quantitative finance program). For more information, see Frey webpage.
Haipeng Xing is a statistician whose research is focused on statistical problem in quantitative, in particular (i) change-points detection, parameter estimation and adaptive control problems and their applications in engineering, economics and genetics; (ii) statistical models and methods in financial econometrics and engineering; and (iii) time series modeling. He is co-author, with T.L. Lai of Stanford, of a widely used textbook on statistical methods in finance. For more information, see Xing webpage.
Stochastic Optimization
Eugene Feinberg works in stochastic methods of operations research and their industrial applications. He is one of the leaders in Markov decision processes and its application to telecommunication, manufacturing, transportation, service and to other man-made systems. He is also one of the country's experts on optimizing electric energy transmission and forecasting energy demand. For more information, see Feinberg webpage.
Jiaqiao Hu's research is focused on designing and analyzing randomized algorithms for solving Markov decision processes and global optimization problems. He has been investigating new sampling and simulation-based techniques to overcome the computational difficulties associated with traditional methods, where sampling and simulation techniques are used not only to avoid enumerating the entire solution space but also to resolve the issue of the unavailability of explicit mathematical models of the underlying systems. For more information, see Hu webpage.