Conic Integer Programming

圆锥整数规划是一个带有圆锥约束的整数规划问题。圆锥约束用于许多工程和科学应用的建模，例如用于疾病诊断的数据的识别和分类，在包括数字成像，通信和金融在内的不同领域中限制风险和错误。该补助金为圆锥整数规划的切割平面算法理论的发展提供资金，以及为解决圆锥整数规划问题的实际应用设计和实施计算方法。将对圆锥整数规划的凸船体结构进行严格的研究。特别是，二阶圆锥整数约束集的圆锥切割平面将通过将其分解为更简单的构建块来开发。如果成功，则该项目的基本开发和解决方法将在涉及风险约束和离散决策的广泛工程和科学应用中非常有用。该项目的直接成果之一将是开发新的切割平面，可用于圆锥混合整数规划的分支定界求解器。预计采用这种削减将大大提高这些软件系统的性能。

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.