Automatic Categorization of Optimization Problems: An Application of Computer Symbolic Mathematics

This paper describes a computer program that accepts as input a symbolic mathematical statement of an arbitrary mathematical programming problem, placing the problem into none or at least one of the categories: linear, quadratic, separable, posynomial, signomial, or convex. This categorization program is intended to reveal properties that can be exploited by special-purpose numerical computer programs—properties that might easily be overlooked because of the size of the problem, the complexity of the problem, or the limited knowledge of a novice who wishes to solve an optimization problem. The paper includes a brief demonstration of the program, a discussion of the underlying techniques, and a summary of the performance for some large problems.