Related papers: Convergence analysis of dynamical systems for opti…
This paper considers a class of nonlinear systems consisting of a linear part with an external input and a nonlinear feedback with a backlash. Assuming that the latter is specified by a strongly convex set, we establish estimates for the…
We study the so-called distributed two-time-scale gradient method for solving convex optimization problems over a network of agents when the communication bandwidth between the nodes is limited, and so information that is exchanged between…
We provide algorithms for computing a Lyapunov function for a class of systems where the state trajectories are constrained to evolve within a closed convex set. The dynamical systems that we consider comprise a differential equation which…
In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…
We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including H\"olderian growth…
While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
In this paper, we conduct a theoretical and numerical study of the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) under strong convexity assumptions. We propose an autonomous Lyapunov function that reflects the strong convexity of…
We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a…
In this paper, we propose a continuous-time primal-dual approach for linearly constrained multiobjective optimization problems. A novel dynamical model, called accelerated multiobjective primal-dual flow, is presented with a second-order…
In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for single-integrator and double-integrator multi-agent systems. Two distributed adaptive optimization algorithm is…
This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…
The aim of this paper is to shed more light on some recent ideas about Lyapunov exponents and clarify the formal structures behind these ideas. In particular, we show that the vector of (averaged) Lyapunov exponents of a smooth…
In Hilbert space, we propose a family of primal-dual dynamical system for affine constrained convex optimization problem. Several damping coefficients, time scaling coefficients, and perturbation terms are thus considered. By constructing…
We introduce and investigate the asymptotic behaviour of the trajectories of a second order dynamical system with Tikhonov regularization for solving a monotone equation with single valued, monotone and continuous operator acting on a real…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides its classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws…