title: Use of proximal operator graph solver for radiation therapy inverse treatment planning.
abstract: OBJECTIVE
  Most radiation therapy optimization problems can be formulated as an unconstrained problem and solved efficiently by quasi-Newton methods such as the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. However, several next generation planning techniques such as total variation regularization- based optimization and MV+kV optimization, involve constrained or mixed-norm optimization, and cannot be solved by quasi-Newton methods. Using standard optimization algorithms on such problems often leads to prohibitively long optimization times and large memory requirements. This work investigates the use of a recently developed proximal operator graph solver (POGS) in solving such radiation therapy optimization problems.
  
  
  METHODS
  Radiation therapy inverse treatment planning was formulated as a graph form problem, and the proximal operators of POGS for quadratic optimization were derived. POGS was exploited for the first time to impose hard dose constraints along with soft constraints in the objective function. The solver was applied to several clinical treatment sites (TG119, liver, prostate, and head&neck), and the results were compared to the solutions obtained by other commercial and non-commercial optimizers.
  
  
  RESULTS
  For inverse planning optimization with nonnegativity box constraints on beamlet intensity, the speed of POGS can compete with that of LBFGSB in some situations. For constrained and mixed-norm optimization, POGS is about one or two orders of magnitude faster than the other solvers while requiring less computer memory.
  
  
  CONCLUSIONS
  POGS was used for solving inverse treatment planning problems involving constrained or mixed-norm formulation on several example sites. This approach was found to improve upon standard solvers in terms of computation speed and memory usage, and is capable of solving traditionally difficult problems, such as total variation regularization-based optimization and combined MV+kV optimization.
authors.affiliation: Department of Radiation and Cellular Oncology, The University of Chicago, Chicago, IL, 60637, USA.
authors.forename: Xinmin
authors.initials: X
authors.lastname: Liu
authors.affiliation: Department of Radiation and Cellular Oncology, The University of Chicago, Chicago, IL, 60637, USA.
authors.forename: Charles
authors.initials: C
authors.lastname: Pelizzari
authors.affiliation: Department of Radiation and Cellular Oncology, The University of Chicago, Chicago, IL, 60637, USA.
authors.forename: Andrew H
authors.initials: AH
authors.lastname: Belcher
authors.affiliation: Department of Radiation and Cellular Oncology, The University of Chicago, Chicago, IL, 60637, USA.
authors.forename: Zachary
authors.initials: Z
authors.lastname: Grelewicz
authors.affiliation: Department of Radiation and Cellular Oncology, The University of Chicago, Chicago, IL, 60637, USA.
authors.forename: Rodney D
authors.initials: RD
authors.lastname: Wiersma
mesh_terms: D000465:Algorithms; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*
keywords: alternating direction method of multipliers; combined MV+kV optimization; constrained optimization; convex optimization; inverse treatment planning; proximal operator graph solver