Piecewise Linear Solution Paths for Parametric Piecewise Quadratic Programs

Recently, pathfollowing algorithms for parametric optimization problems with piecewise linear solution paths have been developed within the field of regularized regression. This paper presents a generalization of these algorithms to a wider class of problems, namely a class of parametric piecewise quadratic programs and related problems. By using pathfollowing algorithms that exploit the piecewise linearity, the entire solution paths can be very efficiently computed. Possible applications include design parameter selection for identification methods such as Direct Weight Optimization.