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We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
Structural stiffness plays an important role in engineering design. The analysis of stiffness requires precise experiments and computational models that can be difficult or time-consuming to procure. A novel relation between modal and…
This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian…
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…
We develop and analyze a stabilization term for cut finite element approximations of an elliptic second order partial differential equation on a surface embedded in $\mathbb{R}^d$. The new stabilization term combines properly scaled normal…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
This article investigates the robustness of gradient descent algorithms under perturbations. The concept of small-disturbance input-to-state stability (ISS) for discrete-time nonlinear dynamical systems is introduced, along with its…
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…
This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…
Training instability in modern deep learning systems is frequently triggered by rare but extreme gradient-norm spikes, which can induce oversized parameter updates, corrupt optimizer state, and lead to slow recovery or divergence. Widely…
It is quite often claimed, and correctly so, that linear methods cannot achieve global stability results for attitude control, and conversely that nonlinear control is essential in order to achieve (almost) globally stable tracking of…
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
Given an objective function that is invariant under an action of a Lie group, we study how its subgradients relate to the orbits of the action. Our main finding is that they satisfy projection formulae analogous to those stemming from the…
This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
This paper presents a non-linear stability analysis for dc-microgrids in both, interconnected mode and island operation with primary control. The proposed analysis is based on the fact that the dynamical model of the grid is a gradient…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
This paper establishes a general topological condition under which the semilocal stability of a set-valued mapping can be exactly determined by its local stability properties. Specifically, we investigate the relationship between the…