arXiv subjects

Guillaume Derval

Publications and source records attributed to Guillaume Derval.

6 recordsLinked to original sources

arXiv2026

Analyzing changes in optimal variables in linear programming with uncertain parameters

Linear problems often include many parameters that may be uncertain. Sensitivity analysis studies how these parameters impact optimal values. Instead of analyzing the objective function, we shift the focus to the optimal values of the variables. Three types of linear modifications are considered: on the cost vector, the right-hand side, and on the constraint matrix. Several theorems establish properties of these modifications, including conditions for continuity of optimal variable values, as well as local convexity and concavity properties.

math.OC↗

arXiv2026

Sensitivity analysis for linear changes of the constraint matrix of a (mixed-integer) linear program

Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly mixed-integer) linear optimisation problems in which the constraint matrix is subject to linear perturbations controlled by a scalar parameter that varies within a given interval. This is a largely unresolved question with the additional burden that the resulting value function may be largely irregular. We propose several bounding techniques that provide formal guarantees on the behaviour of the objective value across the entire parameter range. The proposed bounds rely on tools from robust optimisation, Lagrangian relaxation, and ad-hoc reformulations. Each method is assessed in terms of accuracy, precision, and computational performance. Experimental results on a large benchmark set show that the proposed bounding techniques effectively address this class of problems, delivering strong guarantees and good precision. In addition, we introduce a spatial branch-and-bound algorithm that incorporates these bounds to compute an anytime approximation of the value function within a given error tolerance, and we analyse its computational performance.

math.OC↗

arXiv2026

Efficient LP warmstarting for linear modifications of the constraint matrix

We consider the problem of computing the optimal solution and objective of a linear program under linearly changing linear constraints. The problem studied is given by $\min c^t x \text{ s.t } Ax + λDx \leq b$ where $λ$ belongs to a set of predefined values $Λ$. Based on the information given by a precomputed basis, we present three efficient LP warm-starting algorithms. Each algorithm is either based on the eigenvalue decomposition, the Schur decomposition, or a tweaked eigenvalue decomposition to evaluate the optimal solution and optimal objective of these problems. The three algorithms have an overall complexity $O(pm^2+pmn)$ where $m$ (resp. $n$) is the number of constraints (resp. variables) of the original problem and $p$ the number of values in $Λ$ after an initial preprocessing step. We also provide theorems related to the optimality conditions to verify when a basis is still optimal and a local bound on the objective.

math.OC↗

arXiv2026

ICLF: An Immersive Code Learning Framework based on Git for Teaching and Evaluating Student Programming Projects

Programming projects are essential in computer science education for bridging theory with practice and introducing students to tools like Git, IDEs, and debuggers. However, designing and evaluating these projects (especially in MOOCs)can be challenging. We propose the Immersive Code Learning Framework (ICLF), a scalable Git-based organizational pipeline for managing and evaluating student programming project. Students begin with an existing code base, a practice that is crucial for mirroring real-world software development. Students then iteratively complete tasks that pass predefined tests. The instructor only manages a hidden parent repository containing solutions, which is used to generate an intermediate public repository with these solutions removed via a templating system. Students are invited collaborators on private forks of this intermediate repository, possibly updated throughout the semester whenever the teacher changes the parent repository. This approach reduces grading platform dependency, supports automated feedback, and allows the project to evolve without disrupting student work. Successfully tested over several years, including in an edX MOOC, this organizational pipeline provides transparent evaluation, plagiarism detection, and continuous progress tracking for each student.

cs.CY↗

arXiv2024

Optimal Control of Renewable Energy Communities subject to Network Peak Fees with Model Predictive Control and Reinforcement Learning Algorithms

We propose in this paper an optimal control framework for renewable energy communities (RECs) equipped with controllable assets. Such RECs allow its members to exchange production surplus through an internal market. The objective is to control their assets in order to minimise the sum of individual electricity bills. These bills account for the electricity exchanged through the REC and with the retailers. Typically, for large companies, another important part of the bills are the costs related to the power peaks; in our framework, they are determined from the energy exchanges with the retailers. We compare rule-based control strategies with the two following control algorithms. The first one is derived from model predictive control techniques, and the second one is built with reinforcement learning techniques. We also compare variants of these algorithms that neglect the peak power costs. Results confirm that using policies accounting for the power peaks lead to a significantly lower sum of electricity bills and thus better control strategies at the cost of higher computation time. Furthermore, policies trained with reinforcement learning approaches appear promising for real-time control of the communities, where model predictive control policies may be computationally expensive in practice. These findings encourage pursuing the efforts toward development of scalable control algorithms, operating from a centralised standpoint, for renewable energy communities equipped with controllable assets.

eess.SY↗

arXiv2019

An aggregate learning approach for interpretable semi-supervised population prediction and disaggregation using ancillary data

Census data provide detailed information about population characteristics at a coarse resolution. Nevertheless, fine-grained, high-resolution mappings of population counts are increasingly needed to characterize population dynamics and to assess the consequences of climate shocks, natural disasters, investments in infrastructure, development policies, etc. Dissagregating these census is a complex machine learning, and multiple solutions have been proposed in past research. We propose in this paper to view the problem in the context of the aggregate learning paradigm, where the output value for all training points is not known, but where it is only known for aggregates of the points (i.e. in this context, for regions of pixels where a census is available). We demonstrate with a very simple and interpretable model that this method is on par, and even outperforms on some metrics, the state-of-the-art, despite its simplicity.

cs.LG↗