Research Article

Limited memory solution of bound constrained convex quadratic problems arising in video games

Michael C. Ferris^a1a2, Andrew J. Wathen^a1 and Paul Armand^a3

Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK.

Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, Wisconsin 53706, USA.

Laboratoire XLIM, Université de Limoges, Faculté des Sciences et Techniques, 123, avenue Albert Thomas, 87060 Limoges, France; armand@unilim.fr

Abstract

We describe the solution of a bound constrained convex quadratic problem with limited memory resources. The problem arises 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 a number of ways of solving an equivalent augmented system. Alternative approaches are briefly surveyed, and some recommendations for solving these types of problems are given.

(Received March 30 2005)

(Accepted June 23 2006)

(Online publication June 15 2007)

Key Words:

• Interior point method;
• nonlinear complementarity problem;
• bound constrained problem;
• limited memory method.

Mathematics Subject Classification:

• 90C20;
• 90C51