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The smoothing task is the core of many signal processing applications. It deals with the recovery of a sequence of hidden state variables from a sequence of noisy observations in a one-shot manner. In this work we propose RTSNet, a highly efficient model-based and data-driven smoothing algorithm. RTSNet integrates dedicated trainable models into the flow of the classical Rauch-Tung-Striebel (RTS) smoother, and is able to outperform it when operating under model mismatch and non-linearities while retaining its efficiency and interpretability.

In this paper, we propose a procedure to accelerate the resolution of the well-known ``Elastic-Net'' problem. Our procedure is based on the (partial) identification of the solution support and the reformulation of the original problem into a problem of reduced dimension. The identification of the support leverages the novel concept of ``safe relaxing'' where one aims to identify non-zero coefficients of the solution.

In this paper, we propose a procedure to accelerate the resolution of the well-known ``Elastic-Net'' problem. Our procedure is based on the (partial) identification of the solution support and the reformulation of the original problem into a problem of reduced dimension. The identification of the support leverages the novel concept of ``safe relaxing'' where one aims to identify non-zero coefficients of the solution.

We present a novel screening methodology to safely discard irrelevant nodes within a generic branch-and-bound (BnB) algorithm solving the l0-penalized least-squares problem. Our contribution is a set of two simple tests to detect sets of feasible vectors that cannot yield optimal solutions. This allows to prune nodes of the BnB search tree, thus reducing the overall optimization time. One cornerstone of our contribution is a nesting property between tests at different nodes that allows to implement them with a low computational cost.

We present a novel screening methodology to safely discard irrelevant nodes within a generic branch-and-bound (BnB) algorithm solving the l0-penalized least-squares problem. Our contribution is a set of two simple tests to detect sets of feasible vectors that cannot yield optimal solutions. This allows to prune nodes of the BnB search tree, thus reducing the overall optimization time. One cornerstone of our contribution is a nesting property between tests at different nodes that allows to implement them with a low computational cost.