Limited memory solution of complementarity problems arising in video games

Abstract

We describe the solution of a complementarity problem with limited memory resources. The problem arising from physical simulations occurring within video games. The motivating problem is outlined, along with a simple interior point approach for its solution. Various linear algebra issues arising in the implementation are explored, including preconditioning, ordering and various ways of solving an equivalent augmented system. Alternative approaches are briefly surveyed, and some recommendations for solving these types of problem are given.

This material is based on research partially supported by the Smith Institute, EPSRC Grant GR/M59044, the National Science Foundation Grant CCR-9972372, the Air Force Office of Scientific Research Grant F49620-01-1-0040, and the Guggenheim Foundation.