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X-WR-CALDESC:Chair for Dynamics, Control, Machine Learning and Numerics -Alexander von Humboldt Professorship
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DTSTART;TZID=Europe/Berlin:20261111T140000
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SUMMARY:Strong Regularity and Input-to-state Stability in Nonconvex Optimization Algorithms
DESCRIPTION:Date: Wed. November 11, 2026\nHost: Prof. Dr. Giovanni Fantuzzi, FAU DCN-AvH Chair for Dynamics, Control, Machine Learning and Numerics -Alexander von Humboldt Professorship at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)\nTalk: Strong Regularity and Input-to-state Stability in Nonconvex Optimization Algorithms\nSpeaker: Dr. Torbjørn Cunis\nAffiliation: Universität Stuttgart | University of Michigan\nAbstract. Nonlinear optimization has become increasingly involved in the guidance and control of dynamic systems. Its applications include optimal path planning, collision avoidance, model predictive control, and extremum seeking. This has motivated the development of an algorithmic systems theory, which studies the stability and robustness of optimization algorithms as dynamic systems. This talk focuses on the relationship between input-to-state stability of nonconvex optimization algorithms under perturbation and (strong) metric regularity of the Karush-Kuhn-Tucker system of necessary conditions. Rooted in variational analysis, metric regularity is a notion of Lipschitz stability for a primal-dual solution under perturbations. It has played a prominent role in analyzing Newton-type methods for optimization, including sequential quadratic programming and augmented Lagrangian methods. In my talk, I characterize strong metric regularity by necessary and sufficient optimality conditions. Moreover, I show that strong metric regularity implies, but is stronger than, small-input input-to-state stability of a prototypical Newton method. These results show that regularity of an optimization problem and stability of an optimization algorithms are linked together.\nOur speaker\nTorbjørn Cunis obtained the M.Sc. degree in Automation Engineering in 2016 and his doctoral degree in Systems Theory in 2019. Since 2021, he is a lecturer at the Institute of Flight Mechanics and Controls, University of Stuttgart. He was a researcher at ONERA – The French Aerospace Lab, a research fellow at the Department of Aerospace Engineering, University of Michigan, and a fellow of the Young ZiF at the Centre for interdisciplinary Research, University of Bielefeld. Dr. Cunis is broadly interested in verification methods for dynamical systems and their connections to optimization algorithms. His research focuses on the systems theory of nonconvex optimization algorithms, optimization-based analysis and control methods for nonlinear dynamical systems, and nonlinear sum-of-squares optimization. Dr. Cunis is an Adjunct Assistant Research Scientist at the University of Michigan.\nWHEN\nWed. November 11, 2026 at 14:00H\nWHERE\n[On-site] Friedrich-Alexander-Universität Erlangen-Nürnberg\nRoom H13. Johann-Radon-Hörsaal\nCauerstraße 11, 91058 Erlangen. Bavaria, Germany\nGPS-Koord. 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URL:https://dcn.nat.fau.eu/events/strong-regularity-and-input-to-state-stability-in-nonconvex-optimization-algorithms/
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