Research Interests

My research is in optimization and its applications. A unifying theme in my research is the construction and exploitation of relaxations and approximations in order to obtain solutions of provable quality to optimization problems. Such approaches are essential in prescriptive analytics approaches for big data, where the determination of high-value actions is desired.

One area of interest is in optimization problems with complementarity constraints, where I have worked for several years on methods for determining globally optimal solutions, in collaboration with Jong-Shi Pang.

Another strong interest is in developing methods to use interior point algorithms in cutting plane and column generation methods. I have proved results for these algorithms and also implemented them successfully for various classes of integer programming problems.

A major application area is in the modeling of interdependent infrastructures with Professors Wallace and Sharkey of the ISE department. We focus especially in the context of recovery and restoration after a disaster. Some recent work is in humanitarian logistics.

Other applications are in diverse fields, including support vector regression, asset-liability management, financial optimization, biofuel production, statistical physics, economics, ranking, scheduling, and sport league alignment. Many of these problem classes can be modeled as optimization problems with complementarity constraints, or as integer programs, or as problems with a huge number of variables that can be attacked using column generation techniques. More than that, many current problems of interest are modeled using a combination of all these features, and the techniques that I have developed and continue to develop will remain useful for determining high-quality solutions.

Much more detail can be found in my papers, most of which are available online.

Click here to see a list of selected sites in optimization and operations research.

I have a bibtex database of optimization references available online. A searchable version of this bibliography is also available.

RPI Math

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