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Entropic Regularization of the ℓ 0 Function

In: Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author

Listed:
  • Jonathan M. Borwein

    (University of Goettingen)

  • D. Russell Luke

Abstract

Many problems of interest where more than one solution is possible seek, among these, the one that is sparsest. The objective that most directly accounts for sparsity, the ℓ 0 metric, is usually avoided since this leads to a combinatorial optimization problem. The function $$\|{x\|}_{0}$$ is often viewed as the limit of the ℓ p metrics. Naturally, there have been some attempts to use this as an objective for p small, though this is a nonconvex function for p

Suggested Citation

  • Jonathan M. Borwein & D. Russell Luke, 2011. "Entropic Regularization of the ℓ 0 Function," 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 65-92, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-9569-8_5
    DOI: 10.1007/978-1-4419-9569-8_5
    as

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