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We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…

This work examines the conditions for asymptotic and exponential convergence of saddle flow dynamics of convex-concave functions. First, we propose an observability-based certificate for asymptotic convergence, directly bridging the gap…

This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the…

Adaptive gradient optimizers (AdaGrad), which dynamically adjust the learning rate based on iterative gradients, have emerged as powerful tools in deep learning. These adaptive methods have significantly succeeded in various deep learning…

This paper considers a disturbance attenuation problem for a linear discrete time invariant system under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in terms of relative…

In this paper, we study the simultaneous stability problem of a finite number of locally inter-connected linear subsystems under practical constraints, including asynchronous and aperiodic sampling, time-varying delays, and measurement…

There have been many recent efforts to study accelerated optimization algorithms from the perspective of dynamical systems. In this paper, we focus on the robustness properties of the time-varying continuous-time version of these dynamics.…

For the stochastic multi-armed bandit (MAB) problem from a constrained model that generalizes the classical one, we show that an asymptotic optimality is achievable by a simple strategy extended from the $\epsilon_t$-greedy strategy. We…

In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…

In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…

We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…

Considering the constrained stochastic optimization problem over a time-varying random network, where the agents are to collectively minimize a sum of objective functions subject to a common constraint set, we investigate asymptotic…

We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to infinity and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove the…

In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic…

A systematic approach to finding variational approximation in an otherwise intractable non-conjugate model is to exploit the general principle of convex duality by minorizing the marginal likelihood that renders the problem tractable. While…

In this paper, the moment matching techniques are adopted to obtain reduced-order closed-loop systems with reduced-order controllers that maintain the closed-loop stability and guarantee desired asymptotic performance, after revealing the…

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…

We study the simulated annealing algorithm based on the kinetic Langevin dynamics, in order to find the global minimum of a non-convex potential function. For both the continuous time formulation and a discrete time analogue, we obtain the…

Building upon the technique that we developed earlier for perturbed sweeping processes with convex moving constraints and monotone vector fields (Kamenskii et al, Nonlinear Anal. Hybrid Syst. 30, 2018), the present paper establishes global…

Recently, many machine learning optimizers have been analysed considering them as the asymptotic limit of some differential equations when the step size goes to zero. In other words, the optimizers can be seen as a finite difference scheme…