Constrained quadratic optimization for radiation treatment planning by use of graph form ADMM

The alternating direction method of multipliers (ADMM) is applied to constrained quadratic optimization of intensity-modulated radiation therapy (IMRT) planning. The proximal operator for the ADMM algorithm is developed, and the algorithm is applied to different clinical treatment sites (liver, prostate, and head & neck). The results are compared with the solutions obtained by several other commercial and non-commercial optimizers. The ADMM solver is about one to two orders of magnitude faster than the other solvers, moreover, it requires less computer memory.