A conic integer program is an integer programming problem with conic constraints. Conic constraints are used in modeling many engineering and science applications, such as recognition and classification of data for diagnosis of diseases, bounding risk and error in diverse areas including digital imaging, communication, and finance. This grant provides funding for the development of a theory of cutting plane algorithms for conic integer programming, as well as design and implementation of computational methods for solving practical applications of conic integer programming problems. A rigorous investigation of the convex hull structure of conic integer programs will be performed. In particular, conic cutting planes for the second-order conic integer constraint set will be developed by decomposing it into its simpler building blocks.
If successful, the fundamental development and solution methods that will result from this project will be very useful in a wide range of engineering and science applications involving risk constraints and discrete decisions. One of the immediate outcomes of the project will be the development of novel cutting planes that can be used in branch-and-bound solvers for conic mixed integer programming. The employment of such cuts are expected to improve the performance of these software systems significantly.