Package 'sssp'

Citation for the SSSP algorithm

Description

Returns the citation line for the SSSP algorithm and the Journal of Global Optimization paper.

Usage

sssp_citation()

Value

A character scalar.

Examples

sssp_citation()

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Exact joint sparsity and group sparsity projection

Description

Computes an exact element of $P_{G_r \cap C_s}(v)$. The argument groups must form a disjoint union of all indices of v; R index vectors are 1-based. A numeric vector groups is interpreted as $(|\mathcal{L}_1|,\ldots,|\mathcal{L}_p|)$ for contiguous groups.

Usage

sssp_project(v, groups, r, s, verbose = FALSE)

Arguments

v	Numeric vector $v \in \mathbb{R}^n$.
groups	Group sizes or a list of 1-based index vectors encoding $\mathcal{L}_1,\ldots,\mathcal{L}_p$.
r	Group sparsity level $r$.
s	Sparsity level $s$.
verbose	If TRUE, print a citation-bearing result.

Value

A list with x, the projection, and info, including objective, tuple, selected_groups, n_tuples, and wall_time.

Examples

v <- c(10, -1, 2, 3, 9, 0, -4, -8, 7, 6)
res <- sssp_project(v, c(3, 4, 3), r = 3, s = 6)
res$x
res$info$tuple

## non-uniform groups given as index lists
v2 <- c(4, -3, 5, 2, -6, 1, 7, -8, 0.5, 9, -2, 3)
groups2 <- list(c(1, 4), c(2, 3, 5, 8, 9, 10), c(6, 7, 11, 12))
sssp_project(v2, groups2, r = 2, s = 5)$info$tuple

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Projected gradient descent with the SSSP projection

Description

Applies $x^{k+1} \in P_{G_r \cap C_s}(x^k - \gamma \nabla f(x^k))$ to $f(x)=\frac{1}{2}\|Ax-b\|_2^2$.

Usage

sssp_solve(A, b, groups, r, s, gamma = NULL, max_iter = 200L,
  tol = 1e-06, x0 = NULL, verbose = FALSE)

Arguments

A	Numeric matrix.
b	Numeric response vector.
groups	Group sizes or a list of 1-based index vectors encoding $\mathcal{L}_1,\ldots,\mathcal{L}_p$.
r	Group sparsity level $r$.
s	Sparsity level $s$.
gamma	Step length $\gamma$; if NULL, use $1/\|A\|_2^2$.
max_iter	Maximum iterations.
tol	Relative step stopping tolerance.
x0	Optional initial vector.
verbose	If TRUE, print a citation-bearing result.

Value

A list with x and info.

Examples

set.seed(1)
A <- matrix(rnorm(40 * 12), 40, 12)
x_true <- c(1, 2, 0, 0, 0, 0, 3, 4, 0, 0, 0, 0)
b <- as.vector(A %*% x_true)
res <- sssp_solve(A, b, groups = c(4, 4, 4), r = 2, s = 4)
res$x

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