TY - CHAP

T1 - A linearly convergent algorithm for solving a class of nonconvex/affine feasibility problems

AU - Beck, Amir

AU - Teboulle, Marc

N1 - Publisher Copyright:
© Springer Science+Business Media, LLC 2011.

PY - 2011

Y1 - 2011

N2 - We introduce a class of nonconvex/affine feasibility (NCF) problems 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.

AB - We introduce a class of nonconvex/affine feasibility (NCF) problems 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.

KW - Affine rank minimization

KW - Compressive sensing

KW - Gradient projection algorithm

KW - Inverse problems

KW - Linear rate of convergence

KW - Mutual coherence of a matrix

KW - Nonconvex affine feasibility

KW - Scalable restricted isometry

KW - Sparse signal recovery

UR - http://www.scopus.com/inward/record.url?scp=84976509864&partnerID=8YFLogxK

U2 - 10.1007/978-1-4419-9569-8_3

DO - 10.1007/978-1-4419-9569-8_3

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AN - SCOPUS:84976509864

T3 - Springer Optimization and Its Applications

SP - 33

EP - 48

BT - Springer Optimization and Its Applications

PB - Springer International Publishing

ER -