Related papers: Saddle Flow Dynamics: Observable Certificates and …
We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…
Many works in convex optimization provide rates for achieving a small primal gap. However, this quantity is typically unavailable in practice. In this work, we show that solving a regularized surrogate with algorithms based on simple…
We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in…
We present a computational analysis that establishes the $O(1/K)$ convergence of the distributed gradient tracking method when the objective function is smooth and convex but not strongly convex. The analysis is inspired by recent work on…
Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in…
In this paper, we address robust static anti-windup compensator design and performance analysis for saturated linear closed loops in the presence of nonlinear probabilistic parameter uncertainties via randomized techniques. The proposed…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…
We examine stability properties of primal-dual gradient flow dynamics for composite convex optimization problems with multiple, possibly nonsmooth, terms in the objective function under the generalized consensus constraint. The proposed…
The control of complex systems faces a trade-off between high performance and safety guarantees, which in particular restricts the application of learning-based methods to safety-critical systems. A recently proposed framework to address…
A transformed primal-dual (TPD) flow is developed for a class of nonlinear smooth saddle point system. The flow for the dual variable contains a Schur complement which is strongly convex. Exponential stability of the saddle point is…
This paper tackles the problem of discretizing accelerated optimization flows while retaining their convergence properties. Inspired by the success of resource-aware control in developing efficient closed-loop feedback implementations on…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…
The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the…
In this paper, we propose a class of general second-order primal-dual dynamical systems with Tikhonov regularization and Hessian-driven damping for solving convex-concave bilinear saddle point problems. The proposed dynamical system…
Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. We introduce both time-invariant and time-varying barrier certificates for discrete-time,…
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…
We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…
This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for…
Flow matching (FM) has shown promising results in data-driven planning. However, it inherently lacks formal guarantees for ensuring state and action constraints, whose satisfaction is a fundamental and crucial requirement for the safety and…