Convex parametric piecewise quadratic optimization: Theory and algorithms

In this paper we study the problem of parametric minimization of convex piecewise quadratic functions. Our study provides a unifying framework for convex parametric quadratic and linear programs. Furthermore, it extends parametric optimization algorithms to problems with piecewise quadratic cost functions, paving the way for new applications of parametric optimization in explicit dynamic programming and optimal control with quadratic stage cost.