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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.

Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invariances called the twelvefold way in enumerative combinatorics and develop a method to characterize lossless compression limits. Explicit computations for all twelve settings are carried out for i.i.d. uniform and Bernoulli distributions. Comparisons among settings provide quantitative insight.

Multiple-object tracking (MOT) and classification are core technologies for processing moving point clouds in radar or lidar applications. For accurate object classification, the one-to-one association relationship between the model of each objects' motion (trackers) and the observation sequences including auxiliary features (e.g., radar cross section) is important.