arXiv subjects

Marah-Lisanne Thormann

Publications and source records attributed to Marah-Lisanne Thormann.

3 recordsLinked to original sources

arXiv2026

Faster than Fast-LTS: Robust Regression and Outlier Detection with DC Programming

When datasets contain outliers, robust regression is a well-established alternative to Ordinary Least Squares. A commonly employed robust estimator is Least Trimmed Squares (LTS), which computes the regression coefficients from a subset of observations. Determining the exact solution corresponds to a combinatorial problem with prohibitive computational costs, even for instances of moderate dimension. Thus, the most prevalent approach in practice remains a heuristic known as Fast-LTS. Although the heuristic often performs effectively, certain elements of the approach remain open to improvement. In particular, its core procedure provides robust results only when initialized with a large number of starting points. To address the heuristic's limitations, this paper reformulates the LTS problem as a concave minimization problem subject to a capped simplex constraint, and proposes the successive Boosted Difference of Convex Functions Algorithm (sBDCA) as a solution method. Theoretically, we establish via the Łojasiewicz property that sBDCA converges to a local solution with a linear rate in the fastest case. To ensure robustness from a single initialization in practice, we derive and integrate a problem-specific preconditioning matrix into the algorithmic setup. Building on this theoretical foundation, we conduct numerical studies on various synthetic and real-world datasets to demonstrate the effectiveness of sBDCA with preconditioning. Specifically, we show that our approach is up to 3.25 times faster than Fast-LTS and achieves up to 90% lower objective function values, particularly in high-dimensional settings. As all code is openly available, this paper further provides a practical guide to robust regression in Python.

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arXiv2026

Data-Driven Hull-Fouling Cleaning Schedule Optimization to Reduce Carbon Footprint of Vessels

In response to climate change, the International Maritime Organization has introduced regulatory frameworks to reduce greenhouse gas emissions from international shipping. Compliance with these regulations is increasingly expected from individual shipping companies, compelling vessel operators to lower the CO2 emissions of their fleets while maintaining economic viability. An important step towards achieving this is performing regular hull and propeller cleaning; however, this entails significant costs. As a result, assessing whether ship performance has declined sufficiently to warrant cleaning from an environmental and economic standpoint is a critical task to ensure both long-term viability and regulatory compliance. In this paper, we address this challenge by proposing a novel data-driven dynamic programming approach to optimize vessel cleaning schedules by balancing both environmental and economic considerations. In numerical experiments, we demonstrate the usefulness of our proposed methodology based on real-world sensor data from ten tramp trading vessels. The results confirm that over a four-year period, fuel consumption can be reduced by up to 5%, even when accounting for the costs of one or two additional cleaning events.

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arXiv2025

The Boosted Difference of Convex Functions Algorithm for Value-at-Risk Constrained Portfolio Optimization

A highly relevant problem of modern finance is the design of Value-at-Risk (VaR) optimal portfolios. Due to contemporary financial regulations, banks and other financial institutions are tied to use the risk measure to control their credit, market, and operational risks. Despite its practical relevance, the non-convexity induced by VaR constraints in portfolio optimization problems remains a major challenge. To address this complexity more effectively, this paper proposes the use of the Boosted Difference-of-Convex Functions Algorithm (BDCA) to approximately solve a Markowitz-style portfolio selection problem with a VaR constraint. As one of the key contributions, we derive a novel line search framework that allows the application of the algorithm to Difference-of-Convex functions (DC) programs where both components are non-smooth. Moreover, we prove that the BDCA linearly converges to a Karush-Kuhn-Tucker point for the problem at hand using the Kurdyka-Lojasiewicz property. We also outline that this result can be generalized to a broader class of piecewise-linear DC programs with linear equality and inequality constraints. In the practical part, extensive numerical experiments under consideration of best practices then demonstrate the robustness of the BDCA under challenging constraint settings and adverse initialization. In particular, the algorithm consistently identifies the highest number of feasible solutions even under the most challenging conditions, while other approaches from chance-constrained programming lead to a complete failure in these settings. Due to the open availability of all data sets and code, this paper further provides a practical guide for transparent and easily reproducible comparisons of VaR-constrained portfolio selection problems in Python.

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