We present a finite algorithm for minimizing a piecewise linear convex function augmented with a simple quadratic term. To solve the dual problem, which is of least-squares form with an additional linear term, we include in a standard active-set quadratic programming algorithm a new column-exchange strategy for treating positive semidefinite problems. Numerical results are given for an implementation using the Cholesky factorization.
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Krzysztof C. Kiwiel (1986) studied this question.