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Auxiliary variables are often used to model a convex piecewise linearfunction in the framework of linear optimization. This work shows that suchvariables yield a block diagonal plus low rank structure in the reduced KKTsystem of the dual problem. We show how the structure can be detectedefficiently, and derive the linear algebra formulas for an interior pointmethod which exploit such structure. The structure is detected in 36% of thecases in Netlib. Numerical results on the inverse planning problem in radiationtherapy show an order of magnitude speed-up compared to the state-of-the-artinterior point solver CPLEX, and considerable improvements in dose distributioncompared to current algorithms.

Interior point methods can exploit structure of convex piecewise linear functions with application in radiation therapy