arXiv subjects

Andrés Miniguano-Trujillo

Publications and source records attributed to Andrés Miniguano-Trujillo.

6 recordsLinked to original sources

arXiv2026

The Integrated Vehicle and Pollster Routing Problem

The National Statistics Bureau of Ecuador conducts monthly price surveys to monitor the evolution of the Consumer Price Index, a metric that measures the consumer prices of essential commodities. These surveys are administered across a designated set of stores, with a fleet of vehicles transporting pollsters from the bureau headquarters to the chosen locations. Additionally, pollsters move between stores using walking paths or vehicles to reduce travel time. This paper introduces the Integrated Vehicle and Pollster Routing Problem and presents an integer programming model to effectively schedule pollster visits to selected stores while optimizing the routing of the vehicle fleet. A three-phase algorithm is proposed, and computational experience with real-world instances is presented.

math.OC↗

arXiv2026

Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation

The nonlocal Cahn-Hilliard equation provides a natural extension of the classical model for phase separation by incorporating long-range interactions through a singular convolution kernel. While this formulation admits a rich existence and regularity theory, its numerical approximation remains challenging: discretisation of the nonlocal term leads to dense operators, and the singularity of the kernel requires special treatment in collocation-based schemes. In this work, we develop an efficient and error-controlled numerical framework for the nonlocal Cahn-Hilliard system with constant mobility, logarithmic potential, Newtonian interaction kernel, and no-flux boundary conditions. Our approach is based on a pseudospectral multishape method that accurately approximates the action of singular convolution operators. We present high-resolution numerical solutions for this nonlocal system of equations that can be achieved with limited computational resources.

math.NA↗

arXiv2025

The Newtonian kernel at the intersection of two discs

We present an exact, closed-form expression for the Newtonian potential of the characteristic function associated with two overlapping discs in the plane. This setting naturally arises when discretising nonlocal interaction terms present in models of phase separation, aggregation dynamics, and quantum systems. We characterise the convolution integral as a piecewise function on the distance between the disc centres, with transitions dictated by the geometry of the overlapping region. Additionally, we derive detailed asymptotic expansions for the small-overlap regime, which allows us to provide stable double-precision codes.

math.AP↗

arXiv2025

Efficient nonlocal linear image denoising: Bilevel optimization with Nonequispaced Fast Fourier Transform and matrix-free preconditioning

We present a new approach for nonlocal image denoising, based around the application of an unnormalized extended Gaussian ANOVA kernel within a bilevel optimization algorithm. A critical bottleneck when solving such problems for finely-resolved images is the solution of huge-scale, dense linear systems arising from the minimization of an energy term. We tackle this using a Krylov subspace approach, with a Nonequispaced Fast Fourier Transform utilized to approximate matrix-vector products in a matrix-free manner. We accelerate the algorithm using a novel change of basis approach to account for the (known) smallest eigenvalue-eigenvector pair of the matrices involved, coupled with a simple but frequently very effective diagonal preconditioning approach. We present a number of theoretical results concerning the eigenvalues and predicted convergence behavior, and a range of numerical experiments which validate our solvers and use them to tackle parameter learning problems. These demonstrate that very large problems may be effectively and rapidly denoised with very low storage requirements on a computer.

math.NA↗

arXiv2024

A Constrained Optimisation Framework for Parameter Identification of the SIRD Model

We consider a numerical framework tailored to identifying optimal parameters in the context of modelling disease propagation. Our focus is on understanding the behaviour of optimisation algorithms for such problems, where the dynamics are described by a system of ordinary differential equations associated with the epidemiological SIRD model. Applying an optimise-then-discretise approach, we examine properties of the solution operator and determine existence of optimal parameters for the problem considered. Further, first-order optimality conditions are derived, the solution of which provides a certificate of goodness of fit, which is not always guaranteed with parameter tuning techniques. We then propose strategies for the numerical solution of such problems, based on projected gradient descent, Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), nonmonotone Accelerated Proximal Gradient (nmAPG), and limited memory BFGS trust region approaches. We carry out a thorough computational study for a range of problems of interest, determining the relative performance of these numerical methods. Our results provide insights into the effectiveness of these strategies, contributing to ongoing research into optimising parameters for accurate and reliable disease spread modelling. Moreover, our approach paves the way for calibration of more intricate compartmental models.

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arXiv2024

Optimizing Connected Components Graph Partitioning With Minimum Size Constraints Using Integer Programming and Spectral Clustering Techniques

In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with minimum size, where each subset induces a connected subgraph with minimal edge cost. The problem naturally surges in applications where connectivity is essential, such as cluster detection in social networks, political districting, sports team realignment, and energy distribution. Mixed Integer Programming formulations together with a variety of valid inequalities are demonstrated and computationally tested. An assisted column generation approach by spectral clustering is also proposed for this problem with additional valid inequalities. Finally, the methods are tested for several simulated instances, and computational results are discussed. Overall, the proposed column generation technique enhanced by spectral clustering offers a promising approach to solve clustering and partitioning problems.

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