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 -