Calendar

Posted December 1, 2025
Last modified March 5, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Khai Nguyen, North Carolina State University
On the Structure of Viscosity Solutions to Hamilton–Jacobi Equations

This talk presents regularity results for viscosity solutions to a class of Hamilton-Jacobi equations arising from optimal exit-time problems in nonlinear control systems under a weak controllability condition. A representation formula for proximal supergradients, based on transported normals, is derived, with applications to optimality conditions, the propagation of singularities, and the Hausdorff measure of the singular set.

Posted January 5, 2026
Last modified March 9, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Jonathan How, Massachusetts Institute of Technology AIAA and IEEE Fellow
Resilient Multi-Agent Autonomy: Perception and Planning for Dynamic, Unknown Environments

Unmanned ground and aerial systems hold promise for critical applications, including search and rescue, environmental monitoring, and autonomous delivery. Real-world deployment in safety-critical settings, however, remains challenging due to GPS-denied operation, perceptual uncertainty, and the need for safe trajectory planning in dynamic unknown environments. This talk presents recent advances in planning, control, and perception that together enable robust, scalable, and efficient aerial autonomy. On the planning and control side, I first introduce DYNUS, which enables uncertainty-aware trajectory planning for safe, real-time flight in dynamic and unknown environments. Building on this foundation, MIGHTY performs fully coupled spatiotemporal optimization to generate agile and precise motion by jointly reasoning about path and timing. Together with prior work on Robust MADER, these methods enable fast, safe, multi-robot navigation under uncertainty. On the perception side, I introduce complementary mapping frameworks that support long-term autonomy and planning. GRAND SLAM combines 3D Gaussian splatting with semantic and geometric priors to produce unified scene representations suitable for photorealistic planning. A second example is ROMAN, which builds on ideas from our prior open set mapping work including SOS MATCH and VISTA. ROMAN compresses environments into sparse, object-centric maps that are orders of magnitude smaller than traditional representations, while still enabling accurate re-localization and loop closure under extreme viewpoint changes. I also discuss the interaction between perception and control, with a focus on safety filtering for systems that rely on learned perception models. Finally, I present results from simulation and hardware experiments and conclude with open challenges in building resilient autonomous aerial systems. Together, these advances move us closer to reliable multi-robot autonomy with meaningful real-world impact. [For the speaker's biographical sketch, click here.]

---

Posted January 2, 2026
Last modified March 11, 2026

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Joint Computational Mathematics and Control and Optimization Seminar to Be Held In Person in 233 Lockett Hall and on Zoom (click here to join)

Jia-Jie Zhu, KTH Royal Institute of Technology in Stockholm
Optimization in Probability Space: PDE Gradient Flows for Sampling and Inference

Many problems in machine learning and Bayesian statistics can be framed as optimization problems that minimize the relative entropy between two probability measures. In recent works, researchers have exploited the connection between the (Otto-)Wasserstein gradient flow of the Kullback-Leibler (or KL) divergence and various sampling and inference algorithms, interacting particle systems, and generative models. In this talk, I will first contrast the Wasserstein flow with the Fisher-Rao flows of a few entropy energy functionals, and showcase their distinct analysis properties when working with different relative entropy driving energies, including the reverse and forward KL divergence. Building upon recent advances in the mathematical foundation of the Hellinger-Kantorovich (HK, a.k.a. Wasserstein-Fisher-Rao) gradient flows, I will then show the analysis of the HK flows and its implications in examples of machine learning tasks.

Event contact: Susanne Brenner

Posted February 5, 2026
Last modified February 6, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Wonjun Lee, Ohio State University
Linear Separability in Contrastive Learning via Neural Training Dynamics

The SimCLR method for contrastive learning of invariant visual representations has become extensively used in supervised, semi-supervised, and unsupervised settings, due to its ability to uncover patterns and structures in image data that are not directly present in the pixel representations. However, this success is still not well understood; neither the loss function nor invariance alone explains it. In this talk, I present a mathematical analysis that clarifies how the geometry of the learned latent distribution arises from SimCLR. Despite the nonconvex SimCLR loss and the presence of many undesirable local minimizers, I show that the training dynamics driven by gradient flow tend toward favorable representations. In particular, early training induces clustering in feature space. Under a structural assumption on the neural network, our main theorem proves that the learned features become linearly separable with respect to the ground-truth labels. To support the theoretical insights, I present numerical results that align with the theoretical predictions.

Posted December 27, 2025
Last modified February 25, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Aris Daniilidis, Technische Universität Wien
Variational Stability of Alternating Projections

The alternate projection method is a classical approach to deal with the convex feasibility problem. We shall first show that given two nonempty closed convex sets $A$ and $B$, the consecutive projections $x_{n+1} = PB(PA(x_n))$, $n \ge 1$ produce a self-contacted sequence, providing in particular an alternative way to establish convergence in the finite dimensional case [2]. In infinite dimensions, a regularity condition is required to ensure convergence of the above sequence $\{x_n\}_{n\ge 1}$ [4]. In [3], it was established that a regularity condition from [1] also ensures the variational stability of the above method. In this talk, we shall complete this result and show that variational stability is actually equivalent to the aforementioned regularity assumption. REFERENCES: [1] H. Bauschke, J. Borwein, On the convergence of von Neumann’s alternating projection algorithm for two sets, Set-Valued Anal. 1 (1993), 185–212. [2] A. Bohm, A. Daniilidis, Ubiquitous algorithms in convex optimization generate self-contracted sequences, J. Convex Anal. 29 (2022) 119–128. [3] C. De Bernardi, E. Miglierina, A variational approach to the alternating projections method, J. Global Optim. 81 (2021), 323-350. [4] H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. 57 (2004), 35–61.

Posted January 2, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Behçet Açıkmeşe, University of Washington AIAA and IEEE Fellow
Optimization-Based Design and Control for Next-Generation Aerospace Systems

Next-generation aerospace systems (e.g., asteroid-mining robots, spacecraft swarms, hypersonic vehicles, and urban air mobility) demand autonomy that transcends current limits. These missions require spacecraft to operate safely, efficiently, and decisively in unpredictable environments, where every decision must balance performance, resource constraints, and risk. The core challenge lies in solving complex optimal control problems in real time, while (i) exploiting full system capabilities without violating safety limits, (ii) certifying algorithmic reliability for critical guidance, navigation, and control (GNC) systems, and (iii) co-designing hardware and software subsystems for optimal end-to-end performance. Our solution is optimization-based autonomy. By transforming GNC challenges into structured optimization problems, we achieve provably robust, computationally tractable solutions. This approach has already revolutionized aerospace, e.g., reusable rockets land autonomously via real-time trajectory planning, drones navigate dynamic obstacles, and spacecraft perform precision docking, all powered by algorithms that solve optimization problems with complex physics-based equations and inequalities in milliseconds. Emerging frontiers (such on-orbit satellite servicing, multi-vehicle asteroid exploration, large-scale orbital spacecraft swarms, and global hypersonic transport) push these methods further. Yet barriers remain, e.g., handling non-convex constraints, ensuring solver resilience, large-scale optimization for decision making and co-design, and bridging the gap between theory and flight-ready systems. This talk explores how real-time optimization is rewriting the rules of autonomy, and how researchers can turn these innovations into practice, propelling aerospace engineering into an era where aerospace systems think, adapt, and perform at the edge of the possible.

Posted January 24, 2026

Control and Optimization Seminar Questions or comments?

10:30 am – 11:20 am Note the Special Seminar Time. Zoom (click here to join)

Michael Friedlander, University of British Columbia SIAM Fellow
Seeing Structure Through Duality

Duality is traditionally introduced as a source of bounds and shadow prices. In this talk I emphasize a second role: revealing structure that enables scalable computation. Starting from LP complementary slackness, I describe a generalization called polar alignment that identifies which "atoms" compose optimal solutions in structured inverse problems. The discussion passes through von Neumann's minimax theorem, Kantorovich's resolving multipliers, and Dantzig's simplex method to arrive at sublinear programs, where an adversary selects worst-case costs from a set. The resulting framework unifies sparse recovery, low-rank matrix completion, and signal demixing. Throughout, dual variables serve as certificates that decode compositional structure.

Posted January 5, 2026

Control and Optimization Seminar Questions or comments?

9:30 am – 10:20 am Zoom (click here to join)

Necmiye Ozay, University of Michigan IEEE Fellow, and ONR Young Investigator, NASA Early Career Faculty, and NSF CAREER Awardee
TBA