Path loss prediction is a crucial task for the planning of networks in modern mobile communication systems. Learning machine-based models seem to be a valid alternative to empirical and deterministic methods for predicting the propagation path loss. As learning machine performance depends on the number of input features, a good way to get a more reliable model can be to use techniques for reducing the dimensionality of the data. In this paper we propose a new approach combining learning machines and dimensionality reduction techniques. We report results on a real dataset showing the efficiency of the learning machine-based methodology and the usefulness of dimensionality reduction techniques in improving the prediction accuracy.

Train movements in railway lines are generally controlled by human dispatchers. As disruptions often occur, dispatchers take real-time scheduling and routing decisions in the attempt to minimize deviations from the ocial timetable. This optimization problem is called Train Dispatching. We represent it as a Mixed Integer Linear Programming model, and solve it by a Benders'-like decomposition within a suitable master/slave scheme. Interestingly, the master and the slave problems correspond to a macroscopic and microscopic representation of the railway, recently exploited in heuristic approaches to the problem. The decomposition, along with some new modeling ideas, allowed us to solve real-life instances of practical interest to optimality in short computing time. Automatic dispatching systems based on our macro/micro decomposition-in which both master and slave are solved heuristically-have been in operation in several Italian lines since year 2011. The exact approach described in this paper outperforms such systems on our test-bed of real-life instances. Furthermore, a system based on another version of the exact decomposition approach has been in operation since February 2014 on a line in Norway.

We propose a branch-and-bound algorithm for minimizing a not necessarily convex quadratic function over integer variables. The algorithm is based on lower bounds computed as continuous minima of the objective function over appropriate ellipsoids. In the nonconvex case, we use ellipsoids enclosing the feasible region of the problem. In spite of the nonconvexity, these minima can be computed quickly; the corresponding optimization problems are equivalent to trust-region subproblems. We present several ideas that allow to accelerate the solution of the continuous relaxation within a branch-and-bound scheme and examine the performance of the overall algorithm by computational experiments. Good computational performance is shown especially for ternary instances.

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We consider low-rank semidefinite programming (LRSDP) relaxations of unconstrained quadratic problems (or, equivalently, of Max-Cut problems) that can be formulated as the non-convex nonlinear programming problem of minimizing a quadratic function subject to separable quadratic equality constraints. We prove the equivalence of the LRSDP problem with the unconstrained minimization of a new merit function and we define an efficient and globally convergent algorithm, called SpeeDP, for finding critical points of the LRSDP problem. We provide evidence of the effectiveness of SpeeDP by comparing it with other existing codes on an extended set of instances of the Max-Cut problem. We further include SpeeDP within a simply modified version of the Goemans-Williamson algorithm and we show that the corresponding heuristic SpeeDP-MC can generate high-quality cuts for very large, sparse graphs of size up to a million nodes in a few hours

In this work we define a block decomposition Jacobi-type method for nonlinear optimization problems with one linear constraint and bound constraints on the variables.We prove convergence of the method to stationary points of the problem under quite general assumptions

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