arXiv subjects

Leonardo D. Secchin

Publications and source records attributed to Leonardo D. Secchin.

3 recordsLinked to original sources

arXiv2026

An Angle-Based Algorithmic Framework for the Interval Discretizable Distance Geometry Problem

Distance Geometry is central to protein structure determination from Nuclear Magnetic Resonance data, where distance restraints are naturally uncertain. We study the interval Discretizable Distance Geometry Problem (\textit{i}DDGP) and introduce two angular Branch-and-Prune (BP) frameworks: the interval Angular Branch-and-Prune (\textit{i}ABP) method and its torsion-guided extension, the interval Torsion-angle Branch-and-Prune (\textit{i}TBP) method. Both methods transform interval distance information into angular constraints on circular arcs; \textit{i}ABP uses these constraints to reduce explicit feasibility checks during branching, while \textit{i}TBP further incorporates prescribed torsion-angle intervals to encode local chirality and planarity information. We develop the corresponding geometric foundations and describe a systematic construction of biologically meaningful \textit{i}DDGP instances from Protein Data Bank structures. Computational experiments indicate that \textit{i}ABP improves the embedding-normalized feasible-solution yield relative to interval BP (\textit{i}BP), a standard enumerative BP baseline for \textit{i}DDGP instances, and that both angular methods find feasible realizations for more instances than \textit{i}BP. Moreover, \textit{i}TBP attains the lowest minimum RMSD on all instances for which both angular methods find feasible realizations, highlighting the benefit of incorporating torsion-angle information.

q-bio.BM↗

arXiv2026

A hybrid combinatorial-continuous strategy for solving molecular distance geometry problems

The Molecular Distance Geometry Problem (MDGP) is essential to structural biology, as it seeks to determine three-dimensional protein structures from partial interatomic distances. Its discretizable subclass (DMDGP) admits an exact combinatorial formulation that enables efficient exploration of the search space. However, in practical settings such as Nuclear Magnetic Resonance (NMR) spectroscopy, distances are available only within uncertainty bounds, leading to the interval variant (\emph{i}DMDGP). We propose a hybrid combinatorial--continuous framework for solving the \emph{i}DMDGP. The method combines an enumeration process derived from the DMDGP with a continuous refinement stage that minimizes a nonconvex stress function penalizing deviations from admissible distance intervals. This integration supports a systematic exploration guided by discrete structure and local optimization. The formulation incorporates torsion angle intervals and chirality constraints through an atom ordering that preserves protein-backbone geometry. Numerical experiments show that the approach efficiently reconstructs geometrically valid conformations even under wide distance bounds, whereas most existing studies assume narrow ones.

math.OC↗

arXiv2026

Parallel Newton methods for the continuous quadratic knapsack problem: A Jacobi and Gauss-Seidel tale

The continuous quadratic knapsack (CQK) problem involves minimizing a diagonal convex quadratic function subject to box constraints and a single linear equality constraint. It has numerous applications in resource allocation, multicommodity flow, machine learning, and classical optimization tasks such as Lagrangian relaxation and quasi-Newton updates. In this work, we revisit the semismooth Newton method introduced by Cominetti, Mascarenhas, and Silva. We demonstrate that the method can be significantly improved in two directions. First, for projections onto the simplex or the $\ell_1$-ball, it can incorporate Condat's highly effective initial multiplier guess. Second, it can serve as a flexible foundation for CQK algorithms, allowing for different parallel variants tailored to exploit CPU and GPU computational models. These improvements are implemented in the open-source Julia package \texttt{NewtonCQK.jl}. We present extensive numerical tests comparing this implementation with other state-of-the-art solvers, demonstrating its superior efficiency and scalability.

math.OC↗