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

Author

Listed:
  • Tasnuva Haque

    (University of British Columbia)

  • Yves Lucet

    (University of British Columbia)

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.

Suggested Citation

  • Tasnuva Haque & Yves Lucet, 2018. "A linear-time algorithm to compute the conjugate of convex piecewise linear-quadratic bivariate functions," Computational Optimization and Applications, Springer, vol. 70(2), pages 593-613, June.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:2:d:10.1007_s10589-018-0007-1
    DOI: 10.1007/s10589-018-0007-1
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    References listed on IDEAS

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    1. Bryan Gardiner & Yves Lucet, 2011. "Graph-Matrix Calculus for Computational Convex Analysis," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 243-259, Springer.
    2. Bryan Gardiner & Khan Jakee & Yves Lucet, 2014. "Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions," Computational Optimization and Applications, Springer, vol. 58(1), pages 249-272, May.
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