AbstractID: 8090 Title: An Efficient Relaxation Method for Dose-Volume Constraints in
IMRT
For optimization problems in intensity modulated radiation therapy (IMRT), many models incorporate dose-volume constraints, which
specify a limit on the fraction of normal tissues that may exceed a certain dose. Such constraints make the problem difficult to solve
in terms of algorithmic complexity, make the feasibility space non-convex, and potentially introduce multiple local minima. We
propose a novel semidefinite programming (SDP) relaxation approach to solving these combinatorial problems with a quadratic
objective function. Semidefinite programming is a modern optimization tool that can be used to model problems with a combinatorial
nature. SDP problems can be solved efficiently by fast interior point methods. Because the SDP relaxation is a convex programming
problem, the issue of multiple local minima is avoided. SDP works by “relaxing” the original non-convex problem into a higher
dimensional space in which the problem becomes convex. However, this requires the solution of an optimization problem with a
larger number of variables. SDP has often been shown to outperform other relaxation schemes both in theory and practice. We
discuss the “rounding” process by which the higher-dimensional solution is converted to a solution to the original problem. Initial
numerical results support this method in terms of solution quality and computational efficiency. Computational examples will be
presented.
Partially supported by NCI CA85181 and CMS, Inc.