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Optimal rank-sparsity decomposition

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  • Jon Lee
  • Bai Zou

Abstract

We describe a branch-and-bound (b&b) method aimed at searching for an exact solution of the fundamental problem of decomposing a matrix into the sum of a sparse matrix and a low-rank matrix. Previous heuristic techniques employed convex and nonconvex optimization. We leverage and extend those ideas, within a spatial b&b framework, aimed at exact global optimization. Our work may serve to (i) gather evidence to assess the true quality of the previous heuristic techniques, and (ii) provide software to routinely calculate global optima or at least better solutions for moderate-sized instances coming from applications. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Jon Lee & Bai Zou, 2014. "Optimal rank-sparsity decomposition," Journal of Global Optimization, Springer, vol. 60(2), pages 307-315, October.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:2:p:307-315
    DOI: 10.1007/s10898-013-0128-0
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    References listed on IDEAS

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    1. DE FARIAS, Ismael R. & NEMHAUSER, Georges L., 2003. "A polyhedral study of the cardinality constrained knapsack problem," LIDAM Reprints CORE 1634, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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