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

Amir Beck () and Marc Teboulle
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Amir Beck: Technion Israel Institute of Technology

Chapter Chapter 3 in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 2011, pp 33-48 from Springer

Abstract: 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.

Keywords: Nonconvex affine feasibility; Inverse problems; Gradient projection algorithm; Linear rate of convergence; Scalable restricted isometry; Mutual coherence of a matrix; Sparse signal recovery; Compressive sensing; Affine rank minimization (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-9569-8_3

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DOI: 10.1007/978-1-4419-9569-8_3

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