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A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems

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

Author

Listed:
  • Amir Beck

    (Technion Israel Institute of Technology)

  • Marc Teboulle

Abstract

We introduce a class of nonconvex/affine feasibility problems (NCF), that consists of finding a point in the intersection of affine constraints with a nonconvex closed set. This class captures some interesting fundamental and NP hard problems arising in various application areas such as sparse recovery of signals and affine rank minimization that we briefly review. Exploiting the special structure of (NCF), we present a simple gradient projection scheme which is proven to converge to a unique solution of (NCF) at a linear rate under a natural assumption explicitly given defined in terms of the problem’s data.

Suggested Citation

  • Amir Beck & Marc Teboulle, 2011. "A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems," 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 33-48, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-9569-8_3
    DOI: 10.1007/978-1-4419-9569-8_3
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