Discovering the characteristics of mathematical programs via sampling

It is often important to know more about the characteristics of a mathematical program than the simple imformation that is returned by a solver. For example, to choose an appropriate solution algorithm, one may need to know something about the convexity of the functions in a nonlinear program, or about which constraints are redundant. For the complex model forms, particularly nonlinear programs and mixed-integer programs, random sampling can discover a great deal of information. This paper describes how to discover interesting characteristics of mathematical programs via sampling, and describes solutions to several difficulties that arise in practice. Several new techniques for discovering characteristics and for improving the accuracy of the characterizations are described.