arXiv subjects

Mihai Anitescu

Publications and source records attributed to Mihai Anitescu.

At least 19 recordsLinked to original sources

arXiv2026

Control and Estimation Co-Design via Envelope-Theorem Gradients

Instead of the sequential plant--control--estimator design pipeline, which is in general not optimal, we propose the Control and Estimation Co-Design (ContEst) framework, which poses the entire system design as a single two-stage problem solved by first-order methods. A key enabler is that the gradient of each inner control/estimation optimal cost with respect to the design parameters is available from the dual variables the inner solver already returns, by the envelope theorem: exactly under mild regularity (a unique inner minimizer), and as a subgradient under more relaxed conditions. That is, no differentiation through the optimizer or its optimality conditions is needed. We first present the framework in a linear quadratic Gaussian (LQG) regime, where the control and estimation costs become two semidefinite programs (SDPs) whose design gradients are read from the duals of the Lyapunov constraints. We extend the results to robust ($H_\infty$) formulation to cover worst-case control and filtering problems. We also present an extension to constrained and nonlinear systems, using an extended Kalman filter (eKF) and a local linearization of the information-state dynamics to yield an approximate but convex model predictive control (MPC) problem whose design gradients are read directly from the costates. We apply our methods to a variety of realistic design examples from different fields and report significant design improvements.

eess.SY↗

arXiv2026

Simultaneous improvement of control and estimation for battery management systems

Standard battery management systems treat the control and state estimation problems as decoupled objectives, relying on certainty equivalence controllers that are blind to the varying observability induced by nonlinear open-circuit voltage models. In this paper, we show that for a broad class of objectives, including the peak shaving and valley filling scenarios common in grid-connected energy storage, the expected cost of a stochastic battery system can be exactly parametrized by the conditional mean and covariance of the state of charge. This reformulation reveals a direct coupling between the control input and estimation quality, a coupling that certainty equivalence controllers ignore, and motivates a dual-control approach in which the controller actively reduces estimation uncertainty by driving the state to high observability regions without compromising the control objective. We derive a deterministic surrogate to this stochastic cost and pose the dual-control problem as a computationally tractable model predictive control problem. We validate our approach on a nine-battery system tracking a time-varying reference trajectory. We report simultaneous improvements in tracking cost (a 28\% reduction) and state estimation error (up to 18\% reduction). The estimation improvement is reported across different state estimators: extended Kalman filter, unscented Kalman filter, and a moving horizon estimator, confirming that the estimation improvement of our approach is not restricted to a specific state observer.

eess.SY↗

arXiv2026

Overlapping Schwarz Scheme for Linear-Quadratic Programs in Continuous Time

We present an optimize-then-discretize framework for solving linear-quadratic optimal control problems (OCP) governed by time-inhomogeneous ordinary differential equations (ODEs). Our method employs a modified overlapping Schwarz decomposition based on the Pontryagin Minimum Principle, partitioning the temporal domain into overlapping intervals and independently solving Hamiltonian systems in continuous time. We demonstrate that the convergence is ensured by appropriately updating the boundary conditions of the individual Hamiltonian dynamics. The cornerstone of our analysis is to prove that the exponential decay of sensitivity (EDS) exhibited in discrete-time OCPs carries over to the continuous-time setting. Unlike the discretize-then-optimize approach, our method can flexibly incorporate different numerical integration methods for solving the resulting Hamiltonian two-point boundary-value subproblems, including adaptive-time integrators. A numerical experiment on a linear-quadratic OCP illustrates the practicality of our approach in broad scientific applications.

math.OC↗

arXiv2026

ExaModels.jl: an Algebraic Modeling System for Nonlinear Programming on GPUs

Large-scale nonlinear programs almost always exhibit partially separable and repetitive structure, yet most existing algebraic modeling systems do not take advantage of it. A nonlinear optimization solver queries the objective, the constraints, and their derivatives at every iteration, so the speed of these evaluations bears directly on the overall solution time. We present ExaModels.jl, a Julia-based algebraic modeling system that exploits this structure to evaluate the objective, the constraints, and their derivatives in parallel. At its core is a single-instruction, multiple-data abstraction that represents a nonlinear program as a small number of algebraic patterns, each repeated over many data points. Because the patterns are visible at compile time, a specialized model and derivative evaluation kernel is compiled for each pattern. Applying that kernel independently across the data points maps naturally onto GPU parallelism and, with sufficiently many threads, yields O(1) evaluation time regardless of the number of data points. On the largest instances of the Luksan-Vlcek library, GPU execution speeds up sparse Hessian evaluation by 76x over single-threaded CPU evaluation, and by 30x on COPS and 7.3x on PGLIB-OPF.

math.OC↗

arXiv2026

Condensed Interior-Point Methods for Scalable Nonlinear Programming on GPUs

This paper explores two variants of condensed-space interior-point methods designed for GPUs - HyKKT and LiftedKKT - by analyzing their numerical properties through error analysis and assessing their real-world performance via extensive numerical experiments with a fully GPU-resident software implementation. Traditional implementations of interior-point methods (IPMs) involve solving indefinite augmented KKT systems repeatedly by utilizing direct sparse solvers based on the LBL factorization with sophisticated numerical pivoting strategies. While this method achieves high performance and robustness on CPUs, the serial nature of numerical pivoting presents challenges for effective implementation on GPUs. Recently, multiple condensed-space IPM strategies have emerged to address this issue by transforming the KKT system into a symmetric positive-definite matrix, which is more suitable for factorization on GPUs. In this study, we demonstrate that although the condensed systems show increased ill-conditioning, the inherent structures of the condensed KKT system effectively counterbalance potential accuracy loss in the IPM. Furthermore, we provide numerical results that thoroughly assess the capabilities of a fully GPU-resident nonlinear programming software stack, comprising MadNLP (a filter line-search IPM solver), cuDSS (a direct sparse solver leveraging Cholesky factorization), and ExaModels (a modeling framework), by benchmarking their performance against the pglib-opf and CUTEst libraries. Our findings suggest that the GPU framework holds promise for solving highly sparse large-scale nonlinear programs, such as optimal power flow instances, except for diminished robustness and limited speedups for edge cases observed within CUTEst instances.

math.OC↗

arXiv2026

Harnessing GPU Acceleration in Large-Scale Process Optimization

This paper presents a proof-of-concept workflow for equation-oriented process optimization that runs entirely on a GPU. Process optimization models often incorporate complex interconnected unit operations, dynamics, and uncertainties, resulting in large nonlinear programs that can be computationally demanding for conventional CPU-based solvers. Although emerging GPU-based solvers offer substantial computational benefits, their application to process optimization has been limited by the lack of GPU-compatible process modeling tools. We address this gap by prototyping the GPU-compatible process optimization models using an existing GPU-capable optimization software stack, including ExaModels (algebraic modeling system), MadNLP (optimization solver), and cuDSS (linear solver). ExaModels formulates the process optimization problem in a GPU-compatible way by exposing its repeated algebraic structure, while MadNLP and cuDSS solve the resulting nonlinear program on the GPU. This workflow is demonstrated on a CO2 absorber design problem under feed uncertainty, in which a shared column diameter is minimized subject to equilibrium and hydraulic constraints in all scenarios. For the largest case with 5,000 scenarios and 1.5 million variables, the GPU workflow achieves a speedup of approximately 21\times over a single-threaded CPU baseline using JuMP, Ipopt, and MA57.

math.OC↗

arXiv2026

Parallel Sequential Quadratic Programming with Overlapping Graph Decomposition and Exact Augmented Lagrangian

In this paper, we address the challenge of solving large-scale graph-structured nonlinear programs (gsNLPs) in a scalable manner. GsNLPs are problems in which the objective and constraint functions are associated with nodes on a graph and depend on the variables of adjacent nodes. This graph-structured formulation encompasses various specific instances, such as dynamic optimization, PDE-constrained optimization, multi-stage stochastic optimization, and general network optimization. By leveraging the sequential quadratic programming (SQP) framework, we propose a globally convergent overlapping graph decomposition method to solve large-scale gsNLPs under standard mild regularity conditions on the graph topology. In each iteration, we perform an overlapping graph decomposition to compute an approximate Newton direction in a parallel environment. Then, we select a suitable stepsize and update the primal-dual iterate by performing a backtracking line search on an exact augmented Lagrangian merit function. Built on the exponential decay of sensitivity of gsNLPs, we show that the approximate Newton direction is a descent direction of the augmented Lagrangian, which leads to global convergence with local linear convergence rate. In particular, global convergence is achieved for sufficiently large overlaps, and the local linear convergence rate improves exponentially in terms of the overlap size. Our results match existing state-of-the-art guarantees established for dynamic programs (which simply correspond to linear graphs). We validate the theory on two PDE-constrained problems: a semilinear elliptic problem and a boundary heating problem.

math.OC↗

arXiv2026

Online Covariance Matrix Estimation in Sketched Newton Methods

Given the ubiquity of streaming data, online algorithms have been widely used for parameter estimation, with second-order methods particularly standing out for their efficiency and robustness. In this paper, we study an online sketched Newton method that leverages a randomized sketching technique to perform an approximate Newton step in each iteration, thereby eliminating the computational bottleneck of second-order methods. While existing studies have established the asymptotic normality of sketched Newton methods, a consistent estimator of the limiting covariance matrix remains an open problem. We propose a fully online covariance matrix estimator that is constructed entirely from the Newton iterates and requires no matrix factorization. Compared to covariance estimators for first-order online methods, our estimator for second-order methods is batch-free. We establish the consistency and convergence rate of our estimator, and coupled with asymptotic normality results, we can then perform online statistical inference for the model parameters based on sketched Newton methods. We also discuss the extension of our estimator to constrained problems, and demonstrate its superior performance on regression problems as well as benchmark problems in the CUTEst set.

stat.ML↗

arXiv2026

Dampening parameter distributional shifts under robust control and gain scheduling

Many traditional robust control approaches assume linearity of the system and independence between the system state-input and the parameters of its approximant (possibly lower-order) model. This assumption implies that the application of robust control design to the underlying system introduces no distributional shifts in the parameters of its approximant model. This is generally not true when the underlying system is nonlinear, which may require different approximant models with different parameter distributions when operated at different regions of the state-input space. Therefore, a robust controller has to be robust under the approximant model with parameter distribution that will be experienced in the future data, after applying this control, not the parameter distribution seen in the learning data or assumed in the design. In this paper, we seek a solution to this problem by restricting the newly designed closed-loop system to be consistent with the learning data and slowing down any distributional shifts in the state-input space of the underlying system, and therefore, in the parameter space of its approximant model. In computational terms, the objective of dampening the shifts in the parameter distribution is formulated as a convex semi-definite program that can be solved efficiently by standard software packages. We evaluate the proposed approach on a simple yet telling gain-scheduling problem, which can be equivalently posed as a robust control problem.

eess.SY↗

arXiv2026

Improved Approximation Bounds for Moore-Penrose Inverses of Banded Matrices with Applications to Continuous-Time Linear Quadratic Control

We present improved approximation bounds for the Moore-Penrose inverses of banded matrices, where the bandedness is induced by a metric on the index set. We show that the pseudoinverse of a banded matrix can be approximated by another banded matrix, and the error of approximation is exponentially small in the ratio of the bandwidth of the approximation to that of the original matrix. An intuitive corollary can be obtained: the off-diagonal blocks of the pseudoinverse decay exponentially with the distance between the node sets associated with row and column indices, on the given metric space. Our bounds are expressed in terms of the bound of singular values of the system. For saddle point systems, commonly encountered in optimization, we provide the bounds of singular values associated under standard regularity conditions. Remarkably, our bounds improve previously reported ones and allow us to establish a perturbation bound for continuous-domain optimal control problems by analyzing the asymptotic limit of their finite difference discretization, which has been challenging with previously reported bounds.

math.OC↗

arXiv2025

BOLT: Block-Orthonormal Lanczos for Trace estimation of matrix functions

Efficient matrix trace estimation is essential for scalable computation of log-determinants, matrix norms, and distributional divergences. In many large-scale applications, the matrices involved are too large to store or access in full, making even a single matrix-vector (mat-vec) product infeasible. Instead, one often has access only to small subblocks of the matrix or localized matrix-vector products on restricted index sets. Hutch++ achieves optimal convergence rate but relies on randomized SVD and assumes full mat-vec access, making it difficult to apply in these constrained settings. We propose the Block-Orthonormal Stochastic Lanczos Quadrature (BOLT), which matches Hutch++ accuracy with a simpler implementation based on orthonormal block probes and Lanczos iterations. BOLT builds on the Stochastic Lanczos Quadrature (SLQ) framework, which combines random probing with Krylov subspace methods to efficiently approximate traces of matrix functions, and performs better than Hutch++ in near flat-spectrum regimes. To address memory limitations and partial access constraints, we introduce Subblock SLQ, a variant of BOLT that operates only on small principal submatrices. As a result, this framework yields a proxy KL divergence estimator and an efficient method for computing the Wasserstein-2 distance between Gaussians - both compatible with low-memory and partial-access regimes. We provide theoretical guarantees and demonstrate strong empirical performance across a range of high-dimensional settings.

math.NA↗

arXiv2025

Beyond Low Rank: Fast Low-Rank + Diagonal Decomposition with a Spectral Approach

Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis, and large-scale kernel learning. We introduce an alternating low-rank then diagonal (Alt) algorithm that provably reduces approximation error and significantly outperforms gradient descent while remaining cheaper than majorization-minimization methods~\cite{sun2016majorization}. To scale to large matrices, we develop a randomized LRPD variant that combines fixed-rank Nystrom sketching~\cite{tropp2017fixed} for the low-rank component with Diag++ stochastic diagonal estimation~\cite{baston2022stochastic}. This hybrid algorithm achieves machine precision decomposition error using a number of matrix-vector products far smaller than the ambient dimension, and comes with rigorous non-asymptotic error bounds. On synthetic data, it exactly recovers LRPD structured matrices with high efficiency, and on real-world S&P 500 stock return covariances, where the spectrum decays slowly and strong sector structure exists, it achieves substantially lower error than pure low-rank approximations.

math.NA↗

arXiv2025

Fourier-Enhanced Recurrent Neural Networks for Electrical Load Time Series Downscaling

We present a Fourier-enhanced recurrent neural network (RNN) for downscaling electrical loads. The model combines (i) a recurrent backbone driven by low-resolution inputs, (ii) explicit Fourier seasonal embeddings fused in latent space, and (iii) a self-attention layer that captures dependencies among high-resolution components within each period. Across four PJM territories, the approach yields RMSE lower and flatter horizon-wise than classical Prophet baselines (with and without seasonality/LAA) and than RNN ablations without attention or Fourier features.

cs.LG↗

arXiv2025

GPU Implementation of Second-Order Linear and Nonlinear Programming Solvers

In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS. This paper provides an overview of the state of the art in GPU-based second-order solvers, focusing on pivoting-free interior-point methods for large and sparse linear and nonlinear programs. We begin by highlighting the capabilities and limitations of the currently available GPU-accelerated sparse linear solvers. Next, we discuss different formulations of the Karush-Kuhn-Tucker systems for second-order methods and evaluate their suitability for pivoting-free GPU implementations. We also discuss strategies for computing sparse Jacobians and Hessians on GPUs for nonlinear programming. Finally, we present numerical experiments demonstrating the scalability of GPU-based optimization solvers. We observe speedups often exceeding 10x compared to comparable CPU implementations on large-scale instances when solved up to medium precision. Additionally, we examine the current limitations of existing approaches.

math.OC↗

arXiv2025

Neighborhood Sampling Does Not Learn the Same Graph Neural Network

Neighborhood sampling is an important ingredient in the training of large-scale graph neural networks. It suppresses the exponential growth of the neighborhood size across network layers and maintains feasible memory consumption and time costs. While it becomes a standard implementation in practice, its systemic behaviors are less understood. We conduct a theoretical analysis by using the tool of neural tangent kernels, which characterize the (analogous) training dynamics of neural networks based on their infinitely wide counterparts -- Gaussian processes (GPs). We study several established neighborhood sampling approaches and the corresponding posterior GP. With limited samples, the posteriors are all different, although they converge to the same one as the sample size increases. Moreover, the posterior covariance, which lower-bounds the mean squared prediction error, is uncomparable, aligning with observations that no sampling approach dominates.

cs.LG↗

arXiv2025

Data-conforming data-driven control: avoiding premature generalizations beyond data

Data-driven and adaptive control approaches face the problem of introducing sudden distributional shifts beyond the distribution of data encountered during learning. Therefore, they are prone to invalidating the very assumptions used in their own construction. This is due to the linearity of the underlying system, inherently assumed and formulated in most data-driven control approaches, which may falsely generalize the behavior of the system beyond the behavior experienced in the data. This paper seeks to mitigate these problems by enforcing consistency of the newly designed closed-loop systems with data and slowing down any distributional shifts in the joint state-input space. This is achieved through incorporating affine regularization terms and linear matrix inequality constraints to data-driven approaches, resulting in convex semi-definite programs that can be efficiently solved by standard software packages. We discuss the optimality conditions of these programs and then conclude the paper with a numerical example that further highlights the problem of premature generalization beyond data and shows the effectiveness of our proposed approaches in enhancing the safety of data-driven control methods.

eess.SY↗

arXiv2025

The statistical spread of transmission outages on a fast protection time scale based on utility data

When there is a fault, the protection system automatically removes one or more transmission lines on a fast time scale of less than one minute. The outaged lines form a pattern in the transmission network. We extract these patterns from utility outage data, determine some key statistics of these patterns, and then show how to generate new patterns consistent with these statistics. The generated patterns provide a new and easily feasible way to model the overall effect of the protection system at the scale of a large transmission system. This new generative modeling of protection is expected to contribute to simulations of disturbances in large grids so that they can better quantify the risk of blackouts. Analysis of the pattern sizes suggests an index that describes how much outages spread in the transmission network at the fast timescale.

eess.SY↗

arXiv2025

Weakly-Constrained 4D Var for Downscaling with Uncertainty using Data-Driven Surrogate Models

Dynamic downscaling typically involves using numerical weather prediction (NWP) solvers to refine coarse data to higher spatial resolutions. Data-driven models such as FourCastNet have emerged as a promising alternative to the traditional NWP models for forecasting. Once these models are trained, they are capable of delivering forecasts in a few seconds, thousands of times faster compared to classical NWP models. However, as the lead times, and, therefore, their forecast window, increase, these models show instability in that they tend to diverge from reality. In this paper, we propose to use data assimilation approaches to stabilize them when used for downscaling tasks. Data assimilation uses information from three different sources, namely an imperfect computational model based on partial differential equations (PDE), from noisy observations, and from an uncertainty-reflecting prior. In this work, when carrying out dynamic downscaling, we replace the computationally expensive PDE-based NWP models with FourCastNet in a ``weak-constrained 4DVar framework" that accounts for the implied model errors. We demonstrate the efficacy of this approach for a hurricane-tracking problem; moreover, the 4DVar framework naturally allows the expression and quantification of uncertainty. We demonstrate, using ERA5 data, that our approach performs better than the ensemble Kalman filter (EnKF) and the unstabilized FourCastNet model, both in terms of forecast accuracy and forecast uncertainty.

physics.ao-ph↗