Enrico Gorgone Separating two finite sets of points in a Euclidean space is a fundamental problem in classification. Customarily linear separation is used, but nonlinear separators such as spheres have been shown to have better performances in some tasks, such as edge detection in images. We exploit the relationships between the more general version of the spherical … Read more
This work introduces a complex variant of the timetabling problem, which is motivated by the case of Italian schools. The new requirements enforce to (i) provide the same idle times for teachers, (ii) avoid consecutive \emph{heavy} days, (iii) limit daily multiple lessons for the same class, (iv) introduce shorter time units to differentiate entry and … Read more
We consider polyhedral separation of sets as a possible tool in supervised classification. In particular we focus on the optimization model introduced by Astorino and Gaudioso and adopt its reformulation in Difference of Convex (DC) form. We tackle the problem by adapting the algorithm for DC programming known as DCA. We present the results of … Read more
In this paper, we first present a new extended formulation of the Capacitated Concentrator Location Problem (CCLP) using the notion of cardinality of terminals assigned to a concentrator location. The disaggregated formulation consists of O(mn2) variables and constraints, where m denotes the number of concentrators and n the number of terminals. An immediate benefit of … Read more
We treat the Feature Selection problem in the Support Vector Machine (SVM) framework by adopting an optimization model based on use of the $\ell_0$ pseudo–norm. The objective is to control the number of non-zero components of normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the polyhedral norm $\|.\|_{[k]}$, intermediate … Read more
This paper is motivated by the case of a forwarder in dealing with inland transportation planning from a seaport, where inbound containers from the sea are filled with pallets, which have different destinations in the landside. Although this forwarder does not have or control any vehicle, he is required to plan the assignment of containers … Read more
We discuss a Lagrangian-relaxation-based heuristics for dealing with feature selection in a standard L1 norm Support Vector Machine (SVM) framework for binary classification. The feature selection model we adopt is a Mixed Binary Linear Programming problem and it is suitable for a Lagrangian relaxation approach. Based on a property of the optimal multiplier setting, we … Read more
We propose a modification to the (generalized) bundle scheme for minimization of a convex nondifferentiable sum-function in the case where some of the components are “easy”, that is, they are Lagrangian functions of explicitly known convex programs with “few” variables and constraints. This happens in many practical cases, particularly within applications to combinatorial optimization. In … Read more
We present a bundle method for convex nondifferentiable minimization where the model is a piecewise quadratic convex approximation of the objective function. Unlike standard bundle approaches, the model only needs to support the objective function from below at a properly chosen (small) subset of points, as opposed to everywhere. We provide the convergence analysis for … Read more