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.
AMS 2010 Subject Classification: 90C30, 90C26
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Acknowledgements
We thank two anonymous referees for their useful comments and suggestions. This research was partially supported by the Israel Science Foundation under ISF Grant 489-06.
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Beck, A., Teboulle, M. (2011). A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems. In: Bauschke, H., Burachik, R., Combettes, P., Elser, V., Luke, D., Wolkowicz, H. (eds) Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Springer Optimization and Its Applications(), vol 49. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9569-8_3
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DOI: https://doi.org/10.1007/978-1-4419-9569-8_3
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