Publications

2025

• Discrete non-abelian X-ray transforms
  
  • Gupta Pranav
  • Novikov Roman
  , 2025. We define a discrete version of the non-abelian X-ray transform, going back in particular to Manakov, Zakharov (1981) and Strichartz (1982). We extend to this transform non-overdetermined reconstruction results obtained for the abelian case in the recent article by Novikov, Sharma (2025). In addition, we establish relations with the continuous non-abelian X-ray transform. In this respect, our results include an explicit and exact non-overdetermined layer-stripping reconstruction procedure for piecewise constant matrix-valued functions from their continuous non-abelian X-ray transform. To our knowledge, this result is new even for the classical X-ray transform.
• Order isomorphisms of sup-stable function spaces: Continuous, Lipschitz, c-convex, and beyond
  
  • Aubin-Frankowski Pierre-Cyril
  • Gaubert Stéphane
  Communications in Contemporary Mathematics, World Scientific Publishing, 2025. There have been many parallel streams of research studying order isomorphisms of some specific sets [Formula: see text] of functions from a set [Formula: see text] to [Formula: see text], such as the sets of convex or Lipschitz functions. We develop in this paper a unified approach inspired by [Formula: see text]-convex functions. Our results are obtained highlighting the role of inf and sup-irreducible elements of [Formula: see text] and the usefulness of characterizing them, to subsequently derive the structure of order isomorphisms, and in particular of those commuting with the addition of scalars. We show that in many cases all these isomorphisms [Formula: see text] are of the form [Formula: see text] for a translation [Formula: see text] and a bijective reparametrization [Formula: see text]. Given a reference anti-isomorphism, this characterization then allows to recover all the other anti-isomorphisms. We apply our theory to the sets of [Formula: see text]-convex functions on compact Hausdorff spaces, to the set of lower semicontinuous (convex) functions on a Hausdorff topological vector space and to 1-Lipschitz functions of complete metric spaces. The latter application is obtained using properties of the horoboundary of a metric space. (10.1142/S0219199725500762)
  DOI : 10.1142/S0219199725500762
• Design of experiments for efficient and conform Bayesian learning of seismic fragility curves
  
  • Van Biesbroeck Antoine
  • Feau Cyril
  • Garnier Josselin
  , 2025 (D7). Seismic fragility curves quantify the probability of failure of mechanical structures as a function of a seismic intensity measure (IM) that is derived from the ground motion. Although based on a strong assumption, the probit-lognormal model is very popular among practitioners for estimating such curves. Since their estimates may be compromised when data is scarce, this paper presents a novel adaptive design of experiments (DoE) strategy, within a Bayesian framework, to address this issue. This strategy first takes the reference prior theory as a support, in order to minimize the incorporation of subjectivity in the method. It then proposes a sequential selection of seismic signals that maximizes their impact on the posterior distribution. An application of the method on a case study taken from the nuclear industry is proposed. The results demonstrate that our approach significantly improves the accuracy and robustness of fragility curves estimations, particularly in data-limited scenarios.
• Left heart hemodynamics simulations with fluid-structure interaction and reduced valve modeling
  
  • Ruz Oscar
  • Diaz Jérôme
  • Vidrascu Marina
  • Moireau Philippe
  • Chapelle Dominique
  • Fernández Miguel Angel
  International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2025, 41 (9), pp.e70088. The combination of reduced models of cardiac valve dynamics with a one-way kinematic uncoupling of blood flow and electromechanics is a widespread approach for reducing the complexity of cardiac hemodynamics simulations. This comes however with a number of shortcomings: artificial pressure oscillations, missing isovolumetric phases and valve laws without precise continuous formulation. This paper is aimed at overcoming these three difficulties while still mitigating computational cost. A novel reduced model of valve dynamics is proposed in which unidirectional flow is enforced in a mathematically sound fashion. Artificial pressure oscillations are overcome by considering a fluid-structure interaction model, which couples bi-ventricular electromechanics and blood flow in the left cavities. The interface coupling is solved in a partitioned fashion via an unconditionally stable loosely coupled scheme. A priori energy estimates are derived for both the continuous coupled problem and its numerical approximation. The benefits and limitations of the proposed approaches are illustrated in a comprehensive numerical study. (10.1002/cnm.70088)
  DOI : 10.1002/cnm.70088
• Homogeneous multigrid for hybrid discretizations: application to HHO methods
  
  • Di Pietro Daniele A.
  • Dong Zhaonan
  • Kanschat Guido
  • Matalon Pierre
  • Rupp Andreas
  Numerical Methods for Partial Differential Equations, Wiley, 2025, 41 (5). We prove the uniform convergence of the geometric multigrid V- cycle for hybrid high-order (HHO) and other discontinuous skeletal methods. Our results generalize previously established results for HDG methods, and our multigrid method uses standard smoothers and local solvers that are bounded, convergent, and consistent. We use a weak version of elliptic regularity in our proofs. Numerical experiments confirm our theoretical results. (10.1002/num.70023)
  DOI : 10.1002/num.70023
• Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes
  
  • Collet Pierre
  • Méléard Sylvie
  • San Jaime
  , 2025. In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov processes including diffusion and jumps. We consider the three regimes, critical, subcritical and supercritical. Under suitable hypotheses on the Feynman-Kac semigroup, we prove a new recurrence for the moments and the extinction probability, their time asymptotics and the convergence in law for the measure-valued birth and death process conditioned to non extinction, leading to the existence of Q-process and Yaglom limit (in this infinite dimensional setting). We develop three classes of natural examples where our results apply.
• Convergence analysis of a high-order Multi-scale Finite Element Method (MsFEM) for Stokes flows in heterogeneous media
  
  • Balazi Loïc
  • Allaire Grégoire
  • Omnes Pascal
  , 2025. An enriched non-conforming Multi-scale Finite Element Method (MsFEM) to solve viscous incompressible flow problems in genuine heterogeneous or porous media was proposed in [Q. Feng, G. Allaire, and P. Omnes, Multiscale Model. Simul., 20(1):462-492, 2022]. The main feature of this MsFEM is the consideration of high-order sets of weighting functions: for the velocity, they are polynomials of order n on the faces and of order n-1 in the volume of the elements; for the pressure they are polynomials of order n in the element volume. In the previously cited reference, only the case n = 1 was numerically tested. The present paper proposes the first implementation for the case n = 2 in two and three dimensions. Furthermore, a discrete analysis of this MsFEM applied to the Stokes problem in heterogeneous media is performed. In particular, a first error estimate is obtained, proving the convergence of this MsFEM for the Stokes problem in periodic perforated media. In addition, it has been shown in the previously cited reference, that the continuous local problems involved in this MsFEM are well-posed. Here, their discrete counterparts are also proved to be well-posed, for any n in two dimensions and for n equal to 1 and 2 in three dimensions, with a judicious choice of non-conforming pairs of finite elements.
• Fourier-Laplace transforms in polynomial Ornstein-Uhlenbeck volatility models
  
  • Abi Jaber Eduardo
  • Li Shaun Xiaoyuan
  • Lin Xuyang
  Finance and Stochastics, Springer Verlag (Germany), 2025. We consider the Fourier-Laplace transforms of a {broad} class of polynomial Ornstein-Uhlenbeck (OU) volatility models, including the well-known Stein-Stein, Schöbel-Zhu, one-factor Bergomi, and the recently introduced Quintic OU models motivated by the SPX-VIX joint calibration problem. We show the connection between the joint {Fourier-Laplace} functional of the log-price and the integrated variance, and the solution of an infinite dimensional Riccati equation. Next, under some non-vanishing conditions of the Fourier-Laplace transforms, we establish an existence result for such Riccati equation and we provide a discretized approximation of the joint characteristic functional that is exponentially entire. On the practical side, we develop a numerical scheme to solve the stiff infinite dimensional Riccati equations and demonstrate the efficiency and accuracy of the scheme for pricing SPX options and volatility swaps using Fourier and Laplace inversions, with specific examples of the Quintic OU and the one-factor Bergomi models and their calibration to real market data.
• Hedging with memory: shallow and deep learning with signatures
  
  • Abi Jaber Eduardo
  • Gérard Louis-Amand
  , 2025. <div><p>We investigate the use of path signatures in a machine learning context for hedging exotic derivatives under non-Markovian stochastic volatility models. In a deep learning setting, we use signatures as features in feedforward neural networks and show that they outperform LSTMs in most cases, with orders of magnitude less training compute. In a shallow learning setting, we compare two regression approaches: the first directly learns the hedging strategy from the expected signature of the price process; the second models the dynamics of volatility using a signature volatility model, calibrated on the expected signature of the volatility. Solving the hedging problem in the calibrated signature volatility model yields more accurate and stable results across different payoffs and volatility dynamics.</p></div>
• A Gyromoment Approach for Electron Dynamics in Low-Temperature E × B Plasmas of Hall Thrusters
  
  • Tazakkati Zoubaïr
  • Laguna Alejandro Alvarez
  • Massot Josselin
  • Massot Marc
  • Pichard Teddy
  , 2025. <div><p>We study the electron dynamics in the acceleration region of a Hall thruster (HT). The strong crossed electric and magnetic fields induce both a fast electron cyclotron gyration around the magnetic field lines and a E × B drift. Starting from a Boltzmann-Poisson system, we perform a dimensional analysis to identify the dominant physical effects within this zone. This yields a non-dimensional kinetic equation tailored to the regime of interest, featuring multiple small parameters and a clear scale separation. The fast cyclotron gyration are filtered out through a Hilbert expansion combined with a gyroaveraging operator, yielding a reduced gyrokinetic model. Then a gyrofluid model is derived using a moment method with an entropy-based closure. Owing to the symmetries introduced by the gyroaveraging process, the number of required moments is reduced, and the closure corresponds to an anisotropic Gaussian requiring only four moments: the density, parallel momentum, and two directional temperatures. A numerical strategy using common tools from the literature is provided to handle the remaining small scales. Numerical experiments exhibit promising results for our applications.</p></div>
• Uniform attachment with freezing
  
  • Bellin Étienne
  • Blanc-Renaudie Arthur
  • Kammerer Emmanuel
  • Kortchemski Igor
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2025, 35 (4). In the classical model of random recursive trees, trees are recursively built by attaching new vertices to old ones. What happens if vertices are allowed to freeze, in the sense that new vertices cannot be attached to already frozen ones? We are interested in the impact of freezing on the height of such trees. (10.1214/25-AAP2190)
  DOI : 10.1214/25-AAP2190
• Scaling limit of graph classes through split decomposition
  
  • Bassino Frédérique
  • Bouvel Mathilde
  • Féray Valentin
  • Gerin Lucas
  • Pierrot Adeline
  The Australasian Journal of Combinatorics, Combinatorial Mathematics Society of Australasia (Inc.), 2025, 92 (3), pp.266-319. We prove that Aldous' Brownian CRT is the scaling limit, with respect to the Gromov--Prokhorov topology, of uniform random graphs in each of the three following families of graphs: distance-hereditary graphs, $2$-connected distance-hereditary graphs and $3$-leaf power graphs. Our approach is based on the split decomposition and on analytic combinatorics. (10.48550/arXiv.2207.12253)
  DOI : 10.48550/arXiv.2207.12253
• Deciphering the Replication-Division Coordination in E. coli: A Unified Mathematical framework for Systematic Model Comparison
  
  • Perrin Alexandre
  • Doumic Marie
  • El Karoui Meriem
  • Méléard Sylvie
  , 2025. While significant efforts have been made to model bacterial cell division, few models have incorporated DNA replication into the control of this process. To date, models that attempt to capture the coordination between replication and division cycles are based on fundamentally different assumptions, and yet conflicting results have emerged. As a result, key questions regarding how replication affects cell size at division remain unclear. To address this, we develop in a first part, a robust mathematical framework to study models of coordination of replication and division cycles proposed in the literature. Through theoretical analysis, we highlight necessary and sufficient conditions to apply to replication-agnostic and division-agnostic models to ensure physiologically-coherent behaviors. Then, in a second part, we lead a comprehensive statistical analysis to assess the ability of the models to reproduce the division volume distribution conditioned on cell covariates. This in-depth analysis highlighted remarkable performances of a novel model, yielding promising results for future refinements toward a universal model of replication-division coordination in E. coli. (10.1101/2025.07.25.666816)
  DOI : 10.1101/2025.07.25.666816
• SKADA-Bench: Benchmarking Unsupervised Domain Adaptation Methods with Realistic Validation On Diverse Modalities
  
  • Lalou Yanis
  • Gnassounou Theo
  • Collas Antoine
  • de Mathelin Antoine
  • Kachaiev Oleksii
  • Odonnat Ambroise
  • Moreau Thomas
  • Gramfort Alexandre
  • Flamary Rémi
  Transactions on Machine Learning Research Journal, [Amherst Massachusetts]: OpenReview.net, 2022, 2025, pp.1-48. Unsupervised Domain Adaptation (DA) consists of adapting a model trained on a labeled source domain to perform well on an unlabeled target domain with some data distribution shift. While many methods have been proposed in the literature, fair and realistic evaluation remains an open question, particularly due to methodological difficulties in selecting hyperparameters in the unsupervised setting. With SKADA-bench, we propose a framework to evaluate DA methods on diverse modalities, beyond computer vision task that have been largely explored in the literature. We present a complete and fair evaluation of existing shallow algorithms, including reweighting, mapping, and subspace alignment. Realistic hyperparameter selection is performed with nested cross-validation and various unsupervised model selection scores, on both simulated datasets with controlled shifts and real-world datasets across diverse modalities, such as images, text, biomedical, and tabular data. Our benchmark highlights the importance of realistic validation and provides practical guidance for real-life applications, with key insights into the choice and impact of model selection approaches. SKADA-bench is open-source, reproducible, and can be easily extended with novel DA methods, datasets, and model selection criteria without requiring re-evaluating competitors. SKADA-bench is available on Github: https://github.com/scikit-adaptation/skada-bench.
• Solving bihomogeneous polynomial systems with a zero-dimensional projection
  
  • Bender Matías R
  • Busé Laurent
  • Checa Carles
  • Tsigaridas Elias
  , 2025, pp.206-214. We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points. To compute (with) the 0-dimensional projection and the corresponding quotient ring, we introduce linear maps that greatly extend the classical multiplication maps for zero-dimensional systems, but are not those associated to the elimination ideal; we also call them multiplication maps. We construct them using linear algebra on the restriction of the ideal to a carefully chosen bidegree or, if available, from an arbitrary Gröbner bases. The multiplication maps allow us to compute the elimination ideal of the projection, by generalizing FGLM algorithm to bihomogenous, non-zero dimensional, varieties. We also study their properties, like their minimal polynomials and the multiplicities of their eigenvalues, and show that we can use the eigenvalues to compute numerical approximations of the zero-dimensional projection. Finally, we establish a single exponential complexity bound for computing multiplication maps and Gröbner bases, that we express in terms of the bidegrees of the generators of the corresponding bihomogeneous ideal. (10.1145/3747199.3747563)
  DOI : 10.1145/3747199.3747563
• An optimal transport based embedding to quantify the distance between playing styles in collective sports
  
  • Baouan Ali
  • Rosenbaum Mathieu
  • Pulido Sergio
  Journal of Quantitative Analysis in Sports, De Gruyter, 2025. This study presents a quantitative framework to compare teams in collective sports with respect to their style of play. The style of play is characterized by the team's spatial distribution over a collection of frames. As a first step, we introduce an optimal transport-based embedding to map frames into Euclidean space, allowing for the efficient computation of a distance. Then, building on this frame-level analysis, we leverage quantization to establish a similarity metric between teams based on a collection of frames from their games. For illustration, we present an analysis of a collection of games from the 2021-2022 Ligue 1 season. We are able to retrieve relevant clusters of game situations and calculate the similarity matrix between teams in terms of style of play. Additionally, we demonstrate the strength of the embedding as a preprocessing tool for relevant prediction tasks. Likewise, we apply our framework to analyze the dynamics in the first half of the NBA season in 2015-2016. (10.1515/jqas-2025-0007)
  DOI : 10.1515/jqas-2025-0007
• Federated Majorize-Minimization: Beyond Parameter Aggregation
  
  • Dieuleveut Aymeric
  • Fort Gersende
  • Hegazy Mahmoud
  • Wai Hoi-To
  , 2025. This paper proposes a unified approach for designing stochastic optimization algorithms that robustly scale to the federated learning setting. Our work studies a class of Majorize-Minimization (MM) problems, which possesses a linearly parameterized family of majorizing surrogate functions. This framework encompasses (proximal) gradient-based algorithms for (regularized) smooth objectives, the Expectation Maximization algorithm, and many problems seen as variational surrogate MM. We show that our framework motivates a unifying algorithm called Stochastic Approximation Stochastic Surrogate MM (SA-SSMM), which includes previous stochastic MM procedures as special instances. We then extend SA-SSMM to the federated setting, while taking into consideration common bottlenecks such as data heterogeneity, partial participation, and communication constraints; this yields FedMM. The originality of FedMM is to learn locally and then aggregate information characterizing the surrogate majorizing function, contrary to classical algorithms which learn and aggregate the original parameter. Finally, to showcase the flexibility of this methodology beyond our theoretical setting, we use it to design an algorithm for computing optimal transport maps in the federated setting.
• Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES
  
  • Matalon Pierre
  • Spillane Nicole
  , 2025. The convergence of the GMRES linear solver is notoriously hard to predict. A particularly enlightening result by [Greenbaum, Pták, Strakoš, 1996] is that, given any convergence curve, one can build a linear system for which GMRES realizes that convergence curve. What is even more extraordinary is that the eigenvalues of the problem matrix can be chosen arbitrarily. We build upon this idea to derive novel results about weighted GMRES. We prove that for any linear system and any prescribed convergence curve, there exists a weight matrix M for which weighted GMRES (i.e. GMRES in the inner product induced by M ) realizes that convergence curve, and we characterize the form of M . Additionally, we exhibit a necessary and sufficient condition on M for the simultaneous prescription of two convergence curves, one realized by GMRES in the Euclidean inner product, and the other in the inner product induced by M . These results are then applied to infer some properties of preconditioned GMRES when the preconditioner is applied either on the left or on the right. For instance, we show that any two convergence curves are simultaneously possible for left and right preconditioned GMRES.
• Infinite Dimensional Mean-Field Belavkin Equation: Well-posedness and Derivation
  
  • de Bouard Anne
  • Guo Gaoyue
  • Hérouard Théo
  , 2025. We analyze the mean-field limit of a stochastic Schrödinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described by Belavkin's filtering equation, we derive a mean-field approximation under minimal assumptions, extending prior results limited to bounded operators and finitedimensional settings. By establishing global well-posedness via fixed-point methods-avoiding measure-change techniques-we obtain higher regularity solutions. Furthermore, we prove rigorous convergence to the mean-field limit in an infinitedimensional framework. Our work provides the first derivation of such limits for wave functions in $L^2 (R^d)$, with implications for simulating and controlling large quantum systems.
• Do you precondition on the left or on the right. A poster at DD29.
  
  • Spillane Nicole
  • Szyld Daniel B
  • Matalon Pierre
  , 2025. The idea behind preconditioning is to accelerate a linear solver by providing it with an approximate inverse of the problem matrix. There are two main ways to precondition the problem Ax = b. Letting H be the preconditioner: • either, HAx = Hb is solved (left preconditioning), • or, AHu = b is solved and the solution is x = Hu (right preconditioning). Split preconditioning is also an option. The goal of this poster is to present similarities and differences between left, right and split preconditioning. We also aim to start a conversation about whether there is a best choice and what your practices are when it comes to preconditioning.
• Distilling Foundation Models for Robust and Efficient Models in Digital Pathology
  
  • Filiot Alexandre
  • Dop Nicolas
  • Tchita Oussama
  • Riou Auriane
  • Dubois Rémy
  • Peeters Thomas
  • Valter Daria
  • Scalbert Marin
  • Saillard Charlie
  • Robin Geneviève
  • Olivier Antoine
  , 2025, 15966, pp.162-172. In recent years, the advent of foundation models (FM) for digital pathology has relied heavily on scaling the pre-training datasets and the model size, yielding large and powerful models. While it resulted in improving the performance on diverse downstream tasks, it also introduced increased computational cost and inference time. In this work, we explore the distillation of a large foundation model into a smaller one, reducing the number of parameters by several orders of magnitude. Leveraging distillation techniques, our distilled model, H0-mini, achieves comparable performance to large FMs at a significantly reduced inference cost on HEST and EVA public benchmarks. Additionally, we conduct robustness analyses on the PLISM-WSI dataset and a multi-scanner, multi-staining private breast cancer cohort. We demonstrate that our distilled model reaches excellent robustness to variations in staining and scanning conditions, significantly outperforming other state-of-the-art models. This opens new perspectives to design lightweight and robust models for digital pathology, without compromising on performance. We publicly release H0-mini along with plismbench, the first robustness benchmark of pathology foundation models based on the PLISM dataset. (10.1007/978-3-032-04981-0_16)
  DOI : 10.1007/978-3-032-04981-0_16
• Debiased Multifidelity Approach to Surrogate Modeling in Aerospace Applications
  
  • Gori Giulio
  • Le Maître Olivier P
  • Congedo Pietro Marco
  Journal of Aircraft, American Institute of Aeronautics and Astronautics, 2025, pp.1-14. We propose a multifidelity formulation for generating cokriging surrogates of complex physics models. First, we show that the standard autoregressive recursive approach may be subject to substantial limitations due to possible modeler’s biases/errors. These are inherent to the process of establishing a nested hierarchy concerning the alleged fidelity of the available models. The formulation we propose mitigates this issue. At each hierarchy level, the predictor consists of a linear combination of all previous levels instead of just the underlying one. The methodology implies a slightly higher training cost for the surrogate. However, the higher training cost is acceptable, considering the effort typically required to generate data in aerospace applications. A few artificial tests, including the optimization of a two-dimensional airfoil, illustrate strengths and weaknesses of the approach. (10.2514/1.C037765)
  DOI : 10.2514/1.C037765
• Strategic geometric graphs through mean field games
  
  • Bertucci Charles
  • Rakotomalala Matthias
  SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2025, 63 (4), pp.2577-2604. We exploit the structure of geometric graphs on Riemannian manifolds to analyze strategic dynamic graphs at the limit, when the number of nodes tends to infinity. This framework allows to preserve intrinsic geometrical information about the limiting graph structure, such as the Ollivier curvature. After introducing the setting, we derive a mean field game system, which models a strategic equilibrium between the nodes. It has the usual structure with the distinction of being set on a manifold. Finally, we establish existence and uniqueness of solutions to the system when the Hamiltonian is quadratic for a class of non-necessarily compact Riemannian manifolds, referred to as manifolds of bounded geometry. (10.1137/24M1666471)
  DOI : 10.1137/24M1666471
• GenEO spectral coarse spaces in SPD domain decomposition
  
  • Spillane Nicole
  Numerical Algorithms, Springer Verlag, 2025. Two-level domain decomposition methods are preconditioned Krylov solvers. What separates one- and two-level domain decomposition methods is the presence of a coarse space in the latter. The abstract Schwarz framework is a formalism that allows to define and study a large variety of two-level methods. The objective of this article is to define, in the abstract Schwarz framework, a family of coarse spaces called the GenEO coarse spaces (for Generalized Eigenvalues in the Overlaps). In detail, this work is a generalization of several methods, each of which exists for a particular choice of domain decomposition method. The article both unifies the GenEO theory and extends it to new settings. The proofs are based on an abstract Schwarz theory which now applies to coarse space corrections by projection, and has been extended to consider singular local solves. Bounds for the condition numbers of the preconditioned operators are proved that are independent of the parameters in the problem (e.g., any coefficients in an underlying PDE or the number of subdomains). The coarse spaces are computed by finding low- or high-frequency spaces of some well-chosen generalized eigenvalue problems in each subdomain. The abstract framework is illustrated by defining two-level Additive Schwarz, Neumann-Neumann and Inexact Schwarz preconditioners for a two-dimensional linear elasticity problem. Explicit theoretical bounds as well as numerical results are provided for this example. (10.1007/s11075-025-02166-x)
  DOI : 10.1007/s11075-025-02166-x
• A Continuation Method Based on CMA-ES
  
  • Vu Hoang Nguyen
  • Brockhoff Dimo
  , 2025, pp.439 - 442. In this poster, we showcase a new algorithm for approximating the Pareto set of two-objective (unconstrained) optimization problems based on the idea of continuation. The algorithm tries to move "along" the Pareto set from one single-objective optimum to the other and back via a single-objective reformulation of the two-objective problem and the well-known CMA-ES as single-objective solver. The introduced algorithm BOG-CMA-ES (standing for bi-objective gradient based CMA-ES) is visually analyzed on simple convex-quadratic objective functions and extensively benchmarked on the bbob-biobj test suite of the COCO platform, including comparisons with current state-of-the-art algorithms. (10.1145/3712255.3726645)
  DOI : 10.1145/3712255.3726645