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- W4377200015 abstract "This paper presents an analysis of the NP-hard minimization problem $$min {Vert b - AxVert _2: x in [0,1]^n, | textrm{supp}(x) | le sigma }$$ , where $$textrm{supp}(x) mathrel {mathop :}={i in [n]: x_i ne 0}$$ and $$sigma $$ is a positive integer. The object of investigation is a natural relaxation where we replace $$| textrm{supp}(x) | le sigma $$ by $$sum _i x_i le sigma $$ . Our analysis includes a probabilistic view on when the relaxation is exact. We also consider the problem from a deterministic point of view and provide a bound on the distance between the images of optimal solutions of the original problem and its relaxation under A. This leads to an algorithm for generic matrices $$A in mathbb {Z}^{m times n}$$ and achieves a polynomial running time provided that m and $$Vert AVert _{infty }$$ are fixed." @default.
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- W4377200015 date "2023-01-01" @default.
- W4377200015 modified "2023-10-01" @default.
- W4377200015 title "Sparse Approximation over the Cube" @default.
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- W4377200015 doi "https://doi.org/10.1007/978-3-031-32726-1_4" @default.
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