arXiv subjects

Fabian Bastin

Publications and source records attributed to Fabian Bastin.

5 recordsLinked to original sources

arXiv2026

An augmented Lagrangian algorithm for constrained nonlinear least-squares

We present an algorithm for solving nonlinear least-squares problems subject to a mix of nonlinear and linear constraints. The nonlinear constraints are handled by reformulating the objective as the augmented Lagrangian function while linear constraints are handled directly. Each iteration consists of approximately solving a linearly constrained problem by means of a gradient projection technique. Our approach also involves a structured approximation of the augmented Lagrangian Hessian. We show global convergence of the method and assess the performance through numerical experiments.

math.OC↗

arXiv2026

A survey of trust-region radius update mechanisms. Part I: First-order analysis

We isolate three structural conditions on trust-region radius update rules for smooth unconstrained nonlinear optimisation, and study the class of mechanisms they define. The conditions act on the radius directly: a lower bound relative to the gradient norm, a contraction on unsuccessful iterations, and a controlled expansion on successful ones. A mechanism is \emph{weakly admissible} if it satisfies the first two conditions, and \emph{strongly admissible} if it satisfies the lower bound together with the controlled-expansion condition. Under uniformly bounded model Hessians, weak admissibility yields $\lim_{k\to\infty}\|\nabla f(x_k)\|=0$, and strong admissibility yields the optimal worst-case complexity $O(ε^{-2})$ for first-order stationarity. Strong admissibility extends the convergence guarantee to linearly growing model Hessians. We verify admissibility for five mechanism classes: fixed-factor, step-driven, retrospective, criticality-anchored, and gradient-scaled. Along the way, we prove convergence of the retrospective update under linearly growing model Hessians and revisit the framework of Curtis and Scheinberg (2020), and Wang and Yuan (2022): we extend it to three distinct scaling factors with decoupled step acceptance (covering $η= 0$), and specialise its stochastic version to the deterministic gradient-scaled

math.OC↗

arXiv2025

Analyzing Airline Alliances through Multi-Attribute Graph Partitioning to Maximize Competition and Market Penetration Capability

The air transportation market is highly competitive and dynamic. Airlines often form alliances to expand their network reach, improve operational efficiency, and enhance customer experience. However, the impact of these alliances on market competition and operational efficiency is not fully understood. In this paper, we propose a novel approach to analyze airline alliances using multi\mfabian{-}attribute graph partitioning. We develop metrics to quantify the competitiveness of flight segments and the market penetration capability of airlines based on their alliance memberships. We formulate a bi\mfabian{-}objective optimization problem to maximize both competition and market penetration simultaneously. We also propose algorithms to solve this optimization problem and demonstrate their effectiveness using real-world flight schedule data. Our results provide insights into the structure of airline alliances and their implications for market competition and operational efficiency.

cs.SI↗

arXiv2025

Prediction of airport on-time performance

We investigate the factors contributing to departure and arrival delays at a major international airport and develop predictive models to estimate both the likelihood and duration of delays. Using logistic regression, random forest, and gradient boosting methods, we identify key predictors of flight punctuality, including historical delay rates of flight numbers and airlines, weather conditions, runway traffic, walk time from security to gate, and overall airport congestion. Our models achieve strong inference and predictive performance in both classification and regression tasks, demonstrating the potential for targeted operational interventions to improve on-time performance and providing actionable insights for airport management and airline operations.

physics.soc-ph↗

arXiv2024

Copula-based transferable models for synthetic population generation

Population synthesis involves generating synthetic yet realistic representations of a target population of micro-agents for behavioral modeling and simulation. Traditional methods, often reliant on target population samples, such as census data or travel surveys, face limitations due to high costs and small sample sizes, particularly at smaller geographical scales. We propose a novel framework based on copulas to generate synthetic data for target populations where only empirical marginal distributions are known. This method utilizes samples from different populations with similar marginal dependencies, introduces a spatial component into population synthesis, and considers various information sources for more realistic generators. Concretely, the process involves normalizing the data and treating it as realizations of a given copula, and then training a generative model before incorporating the information on the marginals of the target population. Utilizing American Community Survey data, we assess our framework's performance through standardized root mean squared error (SRMSE) and so-called sampled zeros. We focus on its capacity to transfer a model learned from one population to another. Our experiments include transfer tests between regions at the same geographical level as well as to lower geographical levels, hence evaluating the framework's adaptability in varied spatial contexts. We compare Bayesian Networks, Variational Autoencoders, and Generative Adversarial Networks, both individually and combined with our copula framework. Results show that the copula enhances machine learning methods in matching the marginals of the reference data. Furthermore, it consistently surpasses Iterative Proportional Fitting in terms of SRMSE in the transferability experiments, while introducing unique observations not found in the original training sample.

stat.ML↗