| Summary: | The class of piecewise linear-quadratic (PLQ) functions is a very important
class of functions in convex analysis since the result of most convex
operators applied to a PLQ function is a PLQ function. Although there exists
a wide range of algorithms for univariate PLQ functions, recent work has
focused on extending these algorithms to PLQ functions with more than one
variable. First, we recall a proof in [Convexity, Convergence and Feedback
in Optimal Control, Phd thesis, R. Goebel, 2000] that PLQ functions are
closed under partial conjugate computation. Then we use recent results on
parametric quadratic programming (pQP) to compute the inf-projection of
any multivariate convex PLQ function. We implemented the algorithm for
bivariate PLQ functions, and modi ed it to compute conjugates. We provide
a complete space and time worst-case complexity analysis and show that for
bivariate functions, the algorithm matches the performance of [Computing
the Conjugate of Convex Piecewise Linear-Quadratic Bivariate Functions,
Bryan Gardiner and Yves Lucet, Mathematical Programming Series B, 2011]
while being easier to extend to higher dimensions.
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