A linear-time algorithm to compute the conjugate of convex piecewise linear-quadratic bivariate functions

Tasnuva Haque and Yves Lucet ()
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Tasnuva Haque: University of British Columbia
Yves Lucet: University of British Columbia

Computational Optimization and Applications, 2018, vol. 70, issue 2, No 10, 593-613

Abstract: Abstract We propose the first algorithm to compute the conjugate of a bivariate Piecewise Linear-Quadratic (PLQ) function in optimal linear worst-case time complexity. The key step is to use a planar graph, called the entity graph, not only to represent the entities (vertex, edge, or face) of the domain of a PLQ function but most importantly to record adjacent entities. We traverse the graph using breadth-first search to compute the conjugate of each entity using graph-matrix calculus, and use the adjacency information to create the output data structure in linear time.

Keywords: Legendre–Fenchel transform; Conjugate; Piecewise linear-quadratic functions; Subdifferential; Convex function; Computational convex analysis (CCA); Computer-aided convex analysis (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10589-018-0007-1

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