Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions

Bryan Gardiner, Khan Jakee and Yves Lucet ()

Computational Optimization and Applications, 2014, vol. 58, issue 1, 249-272

Abstract: Piecewise linear-quadratic (PLQ) functions are an important class of functions in convex analysis since the result of most convex operators applied to a PLQ function is a PLQ function. We modify a recent algorithm for computing the convex (Legendre-Fenchel) conjugate of convex PLQ functions of two variables, to compute its partial conjugate i.e. the conjugate with respect to one of the variables. The structure of the original algorithm is preserved including its time complexity (linear time with some approximation and log-linear time without approximation). Applying twice the partial conjugate (and a variable switching operator) recovers the full conjugate. We present our partial conjugate algorithm, which is more flexible and simpler than the original full conjugate algorithm. We emphasize the difference with the full conjugate algorithm and illustrate results by computing partial conjugates, partial Moreau envelopes, and partial proximal averages. Copyright Springer Science+Business Media New York 2014

Keywords: Legendre-Fenchel transform; Convex conjugate; Piecewise linear-quadratic functions; Computational convex analysis; Partial conjugate (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-013-9622-z

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