Metric Regularity and Its Role in the Systems Theory of Nonlinear Optimization

Abstract: 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 (strong) metric regularity of the Karush—Kuhn—Tucker system of necessary conditions in nonlinear optimization. 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 will show that strong metric regularity is equivalent to a notion of small-input input-to-state stability of a prototypical Newton method. I then provide a characterization of strong metric regularity in the form of necessary and sufficient optimality conditions. An application to nonlinear conic optimization and a discussion of more general regularity concepts conclude the talk.

Bio: Torbjørn Cunis received his doctoral degree in systems and control from ISAE-Supaéro, University of Toulouse, in 2019. Before that, he studied computer science, aerospace computer engineering, and automation engineering at the University of Würzburg and RWTH Aachen University and obtained an MSc degree in 2016.Since 2021, he has been a lecturer (Akademischer Rat a.Z.) at the University of Stuttgart Institute of Flight Mechanics and Controls and an adjunct researcher at the University of Michigan Aerospace Department. He was a researcher at ONERA – The French Aerospace Lab (with Laurent Burlion) from 2016 to 2019 and a research fellow at the University of Michigan (with Ilya Kolmanovsky) from 2019 to 2021. His research focuses on algorithmic systems and control theory, with a focus on nonlinear optimization algorithms and verifiable nonlinear control systems. Dr. Cunis is a fellow of the Young ZiF at the Centre for Interdisciplinary Research at the University of Bielefeld.

*** This Event will take place in a hybrid format. The location for in-person attendance will be room 1311 EECS. Attendance will also be available via Zoom.

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Zoom Passcode information is also available upon request to Kristi Rieger([email protected])