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Opticom and the Iterative Combination Technique for Convex Minimisation

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Sparse Grids and Applications - Munich 2012

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 97))

Abstract

Since “A combination technique for the solution of sparse grid problems” Griebel et al. (1992), the sparse grid combination technique has been successfully employed to approximate sparse grid solutions of multi-dimensional problems. In this paper we study the technique for a minimisation problem coming from statistics. Our methods can be applied to other convex minimisation problems. We improve the combination technique by adapting the “Opticom” method developed in Hegland et al. (Linear Algebra Appl 420:249–275, 2007). We also suggest how the Opticom method can be extended to other numerical problems. Furthermore, we develop a new technique of using the combination technique iteratively. We prove this method yields the true sparse grid solution rather than an approximation. We also present numerical results which illustrate our theory.

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Author information

Authors and Affiliations

  1. The Australian National University, Canberra, ACT, Australia

    Matthias Wong & Markus Hegland

Authors
  1. Matthias Wong
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  2. Markus Hegland
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Corresponding author

Correspondence to Matthias Wong .

Editor information

Editors and Affiliations

  1. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Jochen Garcke

  2. Institute for Parallel and Distributed Systems, Universität Stuttgart, Stuttgart, Germany

    Dirk Pflüger

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Wong, M., Hegland, M. (2014). Opticom and the Iterative Combination Technique for Convex Minimisation. In: Garcke, J., Pflüger, D. (eds) Sparse Grids and Applications - Munich 2012. Lecture Notes in Computational Science and Engineering, vol 97. Springer, Cham. https://doi.org/10.1007/978-3-319-04537-5_14

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