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Vincent Guigues

Publications and source records attributed to Vincent Guigues.

At least 19 recordsLinked to original sources
arXiv2026

The method of ellipcenters with momentum and relaxation for convex quadratic minimization

The method of ellipcenters (ME) is a recent technique developed for unconstrained minimization. Its iteration relies only on first order information and consists of building a suitable two-dimensional ellipse that tries to capture intrinsic ill-conditioning of the problem. The center of the ellipse is taken as the next iterate, which justifies the name of the method. ME was already shown to converge linearly when the objective function is smooth and strongly convex. The special case when the objective is quadratic was studied in the first paper on ME and is also the subject of our work here. In this paper, we propose two variants of ME: RelaxME which adds in ME an additional relaxation step at each iteration and MomME which embeds momentum in ME. We prove linear convergence of RelaxME and MomME and, in particular, we show convergence of RelaxME and MomME (and also of ME) in one iteration when the matrix of the quadratic form has only two distinct eigenvalues. Finally, we provide the results of numerical experiments which compare on five optimization problems (and different combinations of parameters defining these problems) ME, RelaxME, and MomME, with 3 other optimizers: the conjugate gradient method [10], Barzilai and Borwein gradient method with long step [2], and the gradient method with adaptive spectral step length [7]. On most instances, MomME provides the smallest number of iterations and conjugate gradient and MomME provide the smallest CPU times and similar CPU times. This opens optimistic possibilities for ME with momentum in broader settings.

math.OC↗
arXiv2026

Bidirectional SDDP with dimension-free complexity for solving strongly convex stochastic dynamic programming equations

We analyze the complexity of Bidirectional Stochastic Dual Dynamic Programming (BSDDP) algorithm applied to multistage stochastic optimization problems with strongly convex cost functions. Under standard regularity assumptions and without discount factor, we establish an explicit complexity bound on the expected number of iterations needed to obtain an epsilon-optimal policy. Our bound depends on the strong convexity constants and Lipschitz constants of the stagewise cost functions but is independent of the dimensionality of the state space. This improves upon the complexity of SDDP for convex problems from (Lan, 2020), particularly when the number of stages is moderate and the state dimension is large. The analysis further reveals that the complexity decreases as the strong convexity of the cost functions increases, highlighting the algorithm efficiency in structured problem instances.

math.OC↗
arXiv2026

Dimension-Free Complexity Guarantees for Dual Dynamic Programming

This paper studies the complexity of a dual dynamic programming (DDP) method for solving a class of convex optimization problems with linear coupling constraints. Existing complexity results based on DDP depend on the dimensions of the state vectors and, in particular, grow exponentially with dimension. The goal of this paper is to establish a complexity bound that is independent of the dimension. Our approach first studies an unconstrained strongly convex problem and develops a flexible framework for DDP, called FDDP, for solving the associated dynamic programming equations, and establishes an iteration-complexity bound for it that is independent of the dimension. A dimension-independent complexity bound for the original linearly constrained problem is then obtained by applying FDDP to a corresponding unconstrained strongly convex problem obtained via smoothing and penalization. Inspired by the literature on bundle methods, FDDP updates lower approximations of cost-to-go functions through a generic procedure that includes both the classical multi-cut DDP and a new two-cut DDP variant as special cases. The two-cut variant maintains only two affine cuts per stage at each iteration, making it more memory-efficient while retaining the same theoretical guarantees. Finally, numerical experiments illustrate the practical behavior of multi-cut and two-cut DDP, including their dependence on problem parameters and their performance relative to a direct quadratic constraint reformulation.

math.OC↗
arXiv2026

The Method of Ellipcenters for strongly convex minimization

This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow capture ill-conditioning of the underlying optimization problem. In the first article on ME, we were able to prove that it converges with linear rate when the objective function is quadratic and strongly convex, while here we derive convergence for any differentiable strongly convex objective. This investigation was inspired by the great performance of ME in quadratic minimization against steepest descent with exact line search, FISTA, Barzilai-Borwein and Conjugate Gradient. The experiments we carry out now, make ME even more attractive from the numerical point of view. On top of that, the theory seems promising for quite more general settings.

math.OC↗
arXiv2026

Policies for the Operation of an Ambulance Fleet under Uncertainty based on a New Preparedness Metric

Two important decisions in the management of an ambulance fleet are ambulance selection decisions and ambulance reassignment decisions. Ambulance selection decisions determine what to do when an emergency call arrives (such as choosing what ambulance to dispatch to the emergency or putting the emergency in a queue of emergencies waiting for an ambulance to be dispatched). Ambulance reassignment decisions determine where to send an ambulance next when it has finished service for an emergency. Making good ambulance selection decisions and ambulance reassignment decisions is challenging because a decision made at a point in time affects the ability of the emergency medical service to respond to future emergencies (that are typically not known when the decision is made). We propose a new preparedness metric that quantifies the ability of the emergency medical service to respond to future emergencies. The preparedness metric can be used to make ambulance selection decisions and ambulance reassignment decisions by solving a tractable optimization problem each time that a decision has to be made. We compare the performance of the resulting method with 9 methods that have been proposed in the literature, based on data from a real emergency medical service for a large city.

math.OC↗
arXiv2026

New operator designs for Halpern iterations with explicit rates under H\"older error bounds

We investigate the asymptotic behavior of Halpern-type iterations applied to quasi-nonexpansive operators arising in best approximation problems over the intersection of finitely many closed convex sets in $\mathbb{R}^n$. Assuming a local decrease condition for the underlying operator and standard requirements on the stepsizes $(\alpha_k) \subset (0,1)$, we first prove strong convergence of the Halpern sequence $x_{k+1} = \alpha_k x_0 + (1-\alpha_k) T x_k$ to the best approximation point $x^\star$ in the intersection set, that is, the metric projection of $x_0$ onto that set. Under the additional assumption that the intersection satisfies a H\"older-type error bound with exponent $\gamma \in (0,1]$, we then derive explicit convergence rates for both feasibility and norm error: the distance from $x_k$ to the intersection set decays like $\mathcal O(\alpha_k^{\gamma/(2-\gamma)})$, while the norm error $\|x_k - x^\star\|$ decays like $\mathcal O(\alpha_k^{\gamma/(4-2\gamma)})$. These results apply to most projection-type operators used in convex feasibility problems (including MAP, CRM/SCCRM, Cimmino and 3PM/A3PM) and extend classical convergence analyses of the Halpern-type iterations by providing explicit, geometry-dependent rates governed by H\"older-type error bounds. Our numerical experiments show that Halpern-type iterations combined with most of these projection-type operators are quicker than Dykstra's algorithm to find the projection of a point in an intersection of ellipsoids or in an intersection of polyhedrons.

math.OC↗
arXiv2025

Introducing the method of ellipcenters, a new first order technique for unconstrained optimization

In this paper, we introduce the Method of Ellipcenters (ME) for unconstrained minimization. At the cost of two gradients per iteration and a line search, we compute the next iterate by setting it as the center of an elliptical interpolation. The idea behind the ellipse built in each step is to emulate the original level curve of the objective function constrained to a suitable two-dimensional affine space, which is determined by the current iterate and two appropriate gradient vectors. We present the method for general unconstrained minimization and carry out a convergence analysis for the case where the objective function is quadratic. In this context, ME enjoys linear convergence with the rate being at least as good as the linear rate of the steepest descent (gradient) method with optimal step. In our experiments, however, ME was much faster than the gradient method with optimal step size. Moreover, ME seems highly competitive in comparison to several well established algorithms, including Nesterov's accelerated gradient, Barzilai-Borwein, and conjugate gradient. The efficiency in terms of both time and number of iterations is stressed even more for ill-conditioned problems. A theoretical feature that might be a reason for this is that ME coincides with Newton for quadratic programs in two-dimensional Euclidean spaces, solving them in one single step. In our numerical tests, convergence in one iteration only was also observed for much larger problem sizes.

math.OC↗
arXiv2025

A User Manual for cuHALLaR: A GPU Accelerated Low-Rank Semidefinite Programming Solver

We present a Julia-based interface to the precompiled HALLaR and cuHALLaR binaries for large-scale semidefinite programs (SDPs). Both solvers are established as fast and numerically stable, and accept problem data in formats compatible with SDPA and a new enhanced data format taking advantage of Hybrid Sparse Low-Rank (HSLR) structure. The interface allows users to load custom data files, configure solver options, and execute experiments directly from Julia. A collection of example problems is included, including the SDP relaxations of the Matrix Completion and Maximum Stable Set problems.

math.OC↗
arXiv2025

Parallel Polyhedral Projection Method for the Convex Feasibility Problem

In this paper, we introduce and study the Parallel Polyhedral Projection Method (3PM) and the Approximate Parallel Polyhedral Projection Method (A3PM) for finding a point in the intersection of finitely many closed convex sets. Each iteration has two phases: parallel projections onto the target sets (exact in 3PM, approximate in A3PM), followed by an exact or approximate projection onto a polyhedron defined by supporting half-spaces. These strategies appear novel, as existing methods largely focus on parallel schemes like Cimmino's method. Numerical experiments demonstrate that A3PM often outperforms both classical and recent projection-based methods when the number of sets is greater than two. Theoretically, we establish global convergence for both 3PM and A3PM without regularity assumptions. Under a Slater condition or error bound, we prove linear convergence, even with inexact projections. Additionally, we show that 3PM achieves superlinear convergence under suitable geometric assumptions.

math.OC↗
arXiv2025

Stochastic Quadratic Dynamic Programming

We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual Dynamic Programming (SDDP) method replacing affine cuts by quadratic cuts. We provide conditions ensuring strong convexity of the recourse functions and prove the convergence of SQDP. In the special case of a single stage deterministic problem, we call QCSC (Quadratic Cuts for Strongly Convex optimization) the method and prove its complexity. Numerical experiments illustrate the performance and correctness of SQDP, with SQDP being much quicker than SDDP for large values of the constants of strong convexity both for a multistage problem and a two-stage assembly recourse model. We also present the results of numerical experiments on deterministic problems where QCSC is much quicker than several popular competing optimizers for solving 6 strongly convex optimization problems from the literature.

math.OC↗
arXiv2025

Parallelizing the Circumcentered-Reflection Method

This paper introduces the Parallelized Circumcentered Reflection Method (P-CRM), a circumcentric approach that parallelizes the Circumcentered Reflection Method (CRM) for solving Convex Feasibility Problems in affine settings. Beyond feasibility, P-CRM solves the best approximation problem for any finite collection of affine subspaces; that is, it not only finds a feasible point but directly computes the projection of an initial point onto the intersection. Within a fully self-contained scheme, we also introduce the Framework for the Simultaneous Projection Method (F-SPM) which includes Cimmino's method as a special case. Theoretical results show that both P-CRM and F-SPM achieve linear convergence. Moreover, P-CRM converges at a rate that is at least as fast as, and potentially superior to, the best convergence rate of F-SPM. As a byproduct, this also yields a new and simplified convergence proof for Cimmino's method. Numerical experiments show that P-CRM is competitive compared to CRM and indicate that it offers a scalable and flexible alternative, particularly suited for large-scale problems and modern computing environments.

math.OC↗
arXiv2025

cuHALLaR: A GPU Accelerated Low-Rank Augmented Lagrangian Method for Large-Scale Semidefinite Programming

This paper introduces cuHALLaR, a GPU-accelerated implementation of the HALLaR method proposed in Monteiro et al. 2024 for solving large-scale semidefinite programming (SDP) problems. We demonstrate how our Julia-based implementation efficiently uses GPU parallelism through optimization of simple, but key, operations, including linear maps, adjoints, and gradient evaluations. Extensive numerical experiments across three SDP problem classes, i.e., maximum stable set, matrix completion, and phase retrieval show significant performance improvements over both CPU implementations and existing GPU-based solvers. For the largest instances, cuHALLaR achieves speedups of 30-140x on matrix completion problems, up to 135x on maximum stable set problems for Hamming graphs with 8.4 million vertices, and 15-47x on phase retrieval problems with dimensions up to 3.2 million. Our approach efficiently handles massive problems with dimensions up to (n,m) equal to (8 million, 300 million) with high precision, solving matrix completion instances with over 8 million rows and columns in just 142 seconds. These results establish cuHALLaR as a very promising GPU-based method for solving large-scale semidefinite programs.

math.OC↗
arXiv2024

Estimation of Spatiotemporal Poisson Processes with Some Missing Location Data

We consider models for spatiotemporal Poisson processes with some missing location data. We discuss four models that make provision for missing location data, and their estimation. The corresponding code is available on GitHub as an extension of LASPATED at https://github.com/vguigues/LASPATED/Missing_Data. We tested our models using the process of emergency call arrivals to an emergency medical service where the emergency reports often omit the location of the emergency. We show the difference made by using models that make provision for missing location data.

stat.ME↗
arXiv2024

Management and Visualization Tools for Emergency Medical Services

This paper describes an online tool for the visualization of medical emergency locations, randomly generated sample paths of medical emergencies, and the animation of ambulance movements under the control of various dispatch methods in response to these emergencies. The tool incorporates statistical models for forecasting emergency locations and call arrival times, the simulation of emergency arrivals and ambulance movement trajectories, and the computation and visualization of performance metrics such as ambulance response time distributions. Data for the Rio de Janeiro Emergency Medical Service are available on the website. A user can upload emergency data for any Emergency Medical Service, and can then use the visualization tool to explore the uploaded data. A user can also use the statistical tools and/or the simulation tool with any of the dispatch methods provided, and can then use the visualization tool to explore the computational output. Future enhancements include the ability of a user to embed additional dispatch algorithms into the simulation; the tool can then be used to visualize the simulation results obtained with the newly embedded algorithms.

cs.HC↗
arXiv2024

New Heuristics for the Operation of an Ambulance Fleet under Uncertainty

The operation of an ambulance fleet involves ambulance selection decisions about which ambulance to dispatch to each emergency, and ambulance reassignment decisions about what each ambulance should do after it has finished the service associated with an emergency. For ambulance selection decisions, we propose four new heuristics: the Best Myopic (BM) heuristic, a NonMyopic (NM) heuristic, and two greedy heuristics (GHP1 and GHP2). Two variants of the greedy heuristics are also considered. We also propose an optimization problem for an extension of the BM heuristic, useful when a call for several patients arrives. For ambulance reassignment decisions, we propose several strategies to choose which emergency in queue to send an ambulance to or which ambulance station to send an ambulance to when it finishes service. These heuristics are also used in a rollout approach: each time a new decision has to be made (when a call arrives or when an ambulance finishes service), a two-stage stochastic program is solved. The proposed heuristics are used to efficiently compute the second stage cost of these problems. We apply the rollout approach with our heuristics to data of the Emergency Medical Service (EMS) of a large city, and show that these methods outperform other heuristics that have been proposed for ambulance dispatch decisions. We also show that better response times can be obtained using the rollout approach instead of using the heuristics without rollout. Moreover, each decision is computed in a few seconds, which allows these methods to be used for the real-time management of a fleet of ambulances.

math.OC↗
arXiv2024

LASPATED: A Library for the Analysis of Spatio-Temporal Discrete Data (User Manual)

This is the User Manual of the LASPATED library. This library is available on GitHub (at https://github.com/vguigues/LASPATED)) and provides a set of tools to analyze spatiotemporal data. A video tutorial for this library is available on Youtube. It is made of a Python package for time and space discretizations and of two packages (one in Matlab and one in C++) implementing the calibration of the probabilistic models for stochastic spatio-temporal data proposed in the companion paper arXiv:2203.16371v2.

stat.CO↗
arXiv2024

Universal subgradient and proximal bundle methods for convex and strongly convex hybrid composite optimization

This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite optimization problems, namely, a composite subgradient type method and a proximal bundle type method. Functional complexity bounds for the two methods are established in terms of the unknown strong convexity parameter. The two proposed methods are universal with respect to all problem parameters, including the strong convexity one, and require no knowledge of the optimal value. Moreover, in contrast to previous works, they do not restart nor use multiple threads.

math.OC↗