Local beam angle optimization with linear programming and gradient search

The optimization of beam angles in IMRT planning is still an open problem, with literature focusing on heuristic strategies and exhaustive searches on discrete angle grids. We show how a beam angle set can be locally refined in a continuous manner using gradient-based optimization in the beam angle space. The gradient is derived using linear programming duality theory. Applying this local search to 100 random initial angle sets of a phantom pancreatic case demonstrates the method, and highlights the many-local- minima aspect of the BAO problem. Due to this function structure, we recommend a search strategy of a thorough global search followed by local refinement at promising beam angle sets. Extensions to nonlinear IMRT formulations are discussed.