Nelson Maculan

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Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in Euclidean space realizing those given distances. We survey the theory of Euclidean distance geometry and its most important(More)
Given an undirected graph G with penalties associated with its vertices and costs associated with its edges, a Prize Collecting Steiner (PCS) tree is either an isolated vertex of G or else any tree of G, be it spanning or not. The weight of a PCS tree equals the sum of the costs for its edges plus the sum of the penalties for the vertices of G not spanned(More)
The Hartree-Fock equations describe atomic and molecular eletronic wave functions, based on the minimization of a functional of the energy. This can be formulated as a constrained global optimization problem involving nonconvex polynomials exhibiting many local minima. The traditional method of solving the Hartree-Fock problem does not provide a guarantee(More)
The Molecular Distance Geometry Problem consists in finding the positions in R of the atoms of a molecule, given some of the inter-atomic distances. We show that under an additional requirement on the given distances (which is realistic from the chemical point of view) this can be transformed to a combinatorial problem. We propose a Branch-and-Prune(More)
Let G = (V,E,Q) be a undirected graph, where V is the set of vertices, E is the set of edges, and Q = {Q1, . . . , Qq} is a partition of V into q subsets. We refer to Q1, . . . , Qq as the components of the partition. The Partition Coloring Problem (PCP) consists of finding a subset V ′ of V with exactly one vertex from each component Q1, . . . , Qq and(More)
A nonconvex mixed-integer programming formulation for the Euclidean Steiner Tree Problem (ESTP) in R is presented. After obtaining separability between integer and continuous variables in the objective function, a Lagrange dual program is proposed. To solve this dual problem (and obtaining a lower bound for ESTP) we use subgradient techniques. In order to(More)