The paper investigates the problem of achieving globally optimal coverage for non-convex grid environments with a network of mobile sensor nodes. A distributed algorithm is proposed to solve the problem, which is locally implementable on individual sensor. That is, each mobile sensor only requires to update its current position to an adjacent location with certain probability relying on its cov...

This paper deals with the convergence aspect of diffusive delay Lotka-Volterra systems with infinite delays. It is well known that such a system has a globally asymptotically stable steady state if the negative feedbacks of the intraspecific competitions are dominant and instantaneous. It is shown here that such a globally asymptotically stable steady state continues to exist even if the instan...

In this paper, we propose a continuous Newton-type method in the form of an ordinary differential equation by combining the negative gradient and Newton’s direction. It is shown that for a general function f(x), our method converges globally to a connected subset of the stationary points of f(x) under some mild conditions; and converges globally to a single stationary point for a real analytic ...

Superlinear convergence of the Newton method for nonsmooth equations requires a “semismoothness” assumption. In this work we prove that locally Lipschitz functions definable in an o-minimal structure (in particular semialgebraic or globally subanalytic functions) are semismooth. Semialgebraic, or more generally, globally subanalytic mappings present the special interest of being γ -order semism...

Since 1965, there has been significant progress in the theoretical study on quasi-Newton methods for solving nonlinear equations, especially in the local convergence analysis. However, the study on global convergence of quasi-Newton methods is relatively fewer, especially for the BFGS method. To ensure global convergence, some merit function such as the squared norm merit function is typically ...

We consider a multidimensional model for the combustion of compressible reacting fluids. The flow is governed by the Navier-Stokes in Eulerian coordinates and the chemical reaction is irreversible and is governed by the Arrhenius kinetics. The existence of globally defined weak solutions is established by using weak convergence methods, compactness and interpolation arguments in the spirit of F...

In this letter, we discuss the dynamics of the Cohen-Grossberg neural networks. We provide a new and relaxed set of sufficient conditions for the Cohen-Grossberg networks to be absolutely stable and exponentially stable globally. We also provide an estimate of the rate of convergence.

A new globally convergent numerical method is developed for some multidimensional Coefficient Inverse Problems for hyperbolic and parabolic PDEs with applications in acoustics, electromagnetics and optical medical imaging. On each iterative step the Dirichlet boundary value problem for a second order elliptic equation is solved. The global convergence is rigorously proven and numerical experime...

In this note, we propose a solution to the well-know problem of ensuring a simultaneous globally convergent online estimation of the state and the frequencies of a sinusoid signal composed of sinusoidal terms. We present an estimator which guarantees global boundedness and convergence of the state and frequencies estimation for all initial conditions and frequencies values.