6 research outputs found
Towards an efficient approach for the nonconvex -ball projection: algorithm and analysis
This paper primarily focuses on computing the Euclidean projection of a
vector onto the ball in which . Such a problem emerges as
the core building block in statistical machine learning and signal processing
tasks because of its ability to promote sparsity. However, efficient numerical
algorithms for finding the projections are still not available, particularly in
large-scale optimization. To meet this challenge, we first derive the
first-order necessary optimality conditions of this problem. Based on this
characterization, we develop a novel numerical approach for computing the
stationary point through solving a sequence of projections onto the reweighted
-balls. This method is practically simple to implement and
computationally efficient. Moreover, the proposed algorithm is shown to
converge uniquely under mild conditions and has a worst-case
convergence rate. Numerical experiments demonstrate the efficiency of our
proposed algorithm.Comment: This work has been submitted and may be published. Copyright may be
transferred without notice, after which this version may no longer be
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