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
The relaxation complexity $\mathrm{rc}(X)$ of the set of integer points $X$ contained in a polyhedron is the smallest number of facets of any polyhedron $P$ such that the integer points in $P$ coincide with $X$. It is a useful tool to investigate the existence of compact linear descriptions of $X$. In this article, we derive … Read more
This paper builds on the premise that the most vulnerable areas or groups of people should be protected from disasters by being given priority in humanitarian operations, particularly when there are limited resources available for disaster management. The basis and the development of the paper are strongly aligned with the United Nations’ Sustainable Development Goals … Read more
The aim of this paper is two-fold: firstly, to present subspace embedding properties for s-hashing sketching matrices, with $s\geq 1$, that are optimal in the projection dimension $m$ of the sketch, namely, $m=O(d)$, where $d$ is the dimension of the subspace. A diverse set of results are presented that address the case when the input … Read more
We consider variational inequalities governed by strongly pseudomonotone vec- tor fields on Hadamard manifolds. The existence and uniqueness results of the solution, linear convergence, error estimates and finite convergence for sequences generated by a mod- ified projection method for solving variational inequalities are investigated. Some examples and numerical experiments are also given to illustrate our … Read more
We consider a multiperiod stochastic capacitated facility location problem under uncertain demand and budget in each period. Using a scenario tree representation of the uncertainties, we formulate a multistage stochastic integer program to dynamically locate facilities in each period and compare it with a two-stage approach that determines the facility locations up front. In the … Read more
MIMO radar plays a key role in autonomous driving, and the similarity waveform constraint is an important constraint for radar waveform design. However, the joint constant-modulus and similarity constraint is a difficult constraint. Only the special case with $\infty$-norm similarity and constant-modulus constraints is tackled by the semidefinite relaxation (SDR) and the successive quadratic refinement … Read more
Binary polynomial optimization is equivalent to the problem of minimizing a linear function over the intersection of the multilinear set with a polyhedron. Many families of valid inequalities for the multilinear set are available in the literature, though giving a polyhedral characterization of the convex hull is not tractable in general as binary polynomial optimization … Read more
A small polygon is a polygon of unit diameter. The maximal perimeter of a convex equilateral small polygon with $n=2^s$ vertices is not known when $s \ge 4$. In this paper, we construct a family of convex equilateral small $n$-gons, $n=2^s$ and $s \ge 4$, and show that their perimeters are within $\pi^4/n^4 + O(1/n^5)$ … Read more
A total coloring of a graph G = (V, E) is an assignment of colors to vertices and edges such that neither two adjacent vertices nor two incident edges get the same color, and, for each edge, the end-points and the edge itself receive different colors. Any valid total coloring induces a partition of the … Read more