arXiv subjects

Fabian Jakob

Publications and source records attributed to Fabian Jakob.

7 recordsLinked to original sources

arXiv2026

Structure, Analysis, and Synthesis of First-Order Algorithms

First-order optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of optimization algorithms by solving robust control problems. In this work, we use the celebrated internal model principle in control theory to structurally factorize convergent composite optimization algorithms into suitable internal models and core subcontrollers. As the key benefit, we reveal that this permits us to synthesize optimization algorithms even if information is transmitted over networks featuring dynamical phenomena such as time delays, channel memory, or crosstalk. Design of certified linearly-convergent algorithms is achieved under bisection either through a nonconvex local search or by alternation of convex semidefinite programs. We demonstrate factorization of existing optimization algorithms and the automated synthesis of new optimization algorithms in the networked setting.

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arXiv2026

Accelerated ADMM: Automated Parameter Tuning and Improved Linear Convergence

This work studies the linear convergence of an accelerated scheme of the Alternating Direction Method of Multipliers (ADMM) for strongly convex and Lipschitz-smooth problems. We use the methodology of expressing the accelerated ADMM as a Lur'e system, i.e., an interconnection of a linear dynamical system in feedback with a slope-restricted operator, and we use Integral Quadratic Constraints to establish linear convergence. In addition, we propose several parameter tuning heuristics and their impact on the convergence rate through numerical analyses. Our new bounds show improved linear convergence rates compared to the vanilla algorithm and previous proposed accelerated variants, which is also empirically validated on a LASSO regression benchmark.

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arXiv2026

A Generalized Plant Perspective on Linear-Convex Feedback Optimization

Feedback optimization is a control approach for driving a dynamical system to the solution of an optimization problem by interconnecting the plant with an algorithm. Existing stability guarantees typically rely on timescale separation, enforced by conservative gain bounds that limit transient performance and require a pre-stabilized plant. This paper revisits the robust control perspective on feedback optimization. We formulate the plant-optimizer interconnection as a generalized plant, where the cost gradients are characterized by Zames--Falb Integral Quadratic Constraints. Classical timescale-separation bounds are recovered as a special case of static multipliers, with dynamic multipliers yielding substantially tighter stability margins. The formulation also enables IQC based synthesis of dynamic output feedback controllers that jointly stabilize the plant and optimize transient performance, with possible model uncertainty absorbed into an uncertainty channel. For constrained problems, the framework extends to dynamic controllers that generalize projected gradient flows. Numerical examples illustrate the benefits and flexibility of the proposed approach.

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arXiv2026

Analysis and Synthesis of Switched Optimization Algorithms

Deployment of optimization algorithms over communication networks face challenges associated with time delays and corruptions. Fixed time delays can destabilize popular gradient-based algorithms, and this degradation is exacerbated by time-varying delays that may arise from packet drops. This work concentrates on the analysis and synthesis of discrete-time optimization algorithms with certified exponential convergence rates that are robust against switched network dynamics between the optimizer and the gradient oracle. Analysis is accomplished by solving linear matrix inequalities under bisection in the exponential convergence rate, searching over Zames-Falb filter coefficients that can certify convergence. Synthesis is performed by alternating between a search over filter coefficient for a fixed controller, and a search over controllers for a fixed filter. Effectiveness is demonstrated by the synthesis of convergent optimization algorithms over networks with time-varying delays, and networks with unstable channel dynamics.

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arXiv2026

A Linear Parameter-Varying Framework for the Analysis of Time-Varying Optimization Algorithms

In this paper we propose a framework to analyze iterative first-order optimization algorithms for time-varying convex optimization. We assume that the temporal variability is caused by a time-varying parameter entering the objective, which can be measured at the time of decision but whose future values are unknown. We consider the case of strongly convex objective functions with Lipschitz continuous gradients under a convex constraint set. We model the algorithms as discrete-time linear parameter varying (LPV) systems in feedback with monotone operators such as the time-varying gradient. We leverage the approach of analyzing algorithms as uncertain control interconnections with integral quadratic constraints (IQCs) and generalize that framework to the time-varying case. We propose novel IQCs that are capable of capturing the behavior of time-varying nonlinearities and leverage techniques from the LPV literature to establish novel bounds on the tracking error. Quantitative bounds can be computed by solving a semi-definite program and can be interpreted as an input-to-state stability result with respect to a disturbance signal which increases with the temporal variability of the problem. As a departure from results in this research area, our bounds introduce a dependence on different additional measures of temporal variations, such as the function value and gradient rate of change. We exemplify our main results with numerical experiments that showcase how our analysis framework is able to capture convergence rates of different first-order algorithms for time-varying optimization through the choice of IQC and rate bounds.

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arXiv2025

Adaptive Time-Domain Harmonic Control for Noise-Vibration-Harshness Reduction of Electric Drives

Reducing Noise, Vibration, and Harshness (NVH) in electric drives is crucial for applications such as electric vehicle drivetrains and heat-pump compressors, where strict NVH requirements directly affect user satisfaction and component longevity. This work presents the integration of an adaptive time-domain harmonic controller into an existing electric-drive control loop to attenuate harmonic disturbances. Three control structures are proposed and analyzed, along with a modified parameter-estimation scheme that reduces computational effort while preserving estimation accuracy, making the method suitable for embedded real-time implementation. To cope with fast operating-point changes, a delta-learning approach combines adaptive control with a lookup-table-based feedforward estimator, ensuring fast convergence and robustness. The proposed controller architectures are validated through simulation and testbench experiments on a permanent-magnet synchronous machine drive, demonstrating substantial NVH reductions across operating conditions. The results confirm that time-domain adaptive harmonic control offers a practical and theoretically grounded solution for real-time NVH mitigation in electric drives.

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arXiv2025

Online Convex Optimization and Integral Quadratic Constraints: An automated approach to regret analysis

We propose a novel approach for analyzing dynamic regret of first-order constrained online convex optimization algorithms for strongly convex and Lipschitz-smooth objectives. Crucially, we provide a general analysis that is applicable to a wide range of first-order algorithms that can be expressed as an interconnection of a linear dynamical system in feedback with a first-order oracle. By leveraging Integral Quadratic Constraints (IQCs), we derive a semi-definite program which, when feasible, provides a regret guarantee for the online algorithm. For this, the concept of variational IQCs is introduced as the generalization of IQCs to time-varying monotone operators. Our bounds capture the temporal rate of change of the problem in the form of the path length of the time-varying minimizer and the objective function variation. In contrast to standard results in OCO, our results do not require nerither the assumption of gradient boundedness, nor that of a bounded feasible set. Numerical analyses showcase the ability of the approach to capture the dependence of the regret on the function class condition number.

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