In this paper, we propose a general smoothing Broyden-like quasi-Newton method for solving a class of nonsmooth equations. Under appropriate conditions, the proposed method converges to a solution of the equation globally and superlinearly. In particular, the proposed method provides the possibility of developing a quasi-Newton method that enjoys superlinear convergence even if strict complemen...

This paper investigates global asymptotic stability (GAS) and global exponential stability (GES) of a class of continuous-time recurrent neural networks. First, we introduce a necessary and sufficient condition for existence and uniqueness of equilibrium of the neural networks with Lipschitz continuous activation functions. Next, we present two sufficient conditions to ascertain the GAS of the ...

We first generalize, in an abstract framework, results on the order of convergence of a semi-discretization in time by an implicit Euler scheme of a stochastic parabolic equation. In this part, all the coefficients are globally Lipchitz. The case when the nonlinearity is only locally Lipchitz is then treated. For the sake of simplicity, we restrict our attention to the Burgers equation. We are ...

In this paper we solve the problem of computing exact continuous optimal curves and surfaces for image segmentation and 3D reconstruction, using a maximal flow approach expressed by means of a PDE model. Previously existing techniques yield either grid-biased (graph-based approaches) or sub-optimal answers (active contours and surfaces). The proposed algorithm simulates the flow of an ideal flu...

We address the problem of the weights design for consensus algorithms under random network topology. We differ two different cases: 1) high estimate precision is required, and there is no firm restriction on the number of available iterations; 2) there is only a small, limited budget of iterations available. For the first case, we show that minimizing the mean squared error contraction factor i...

In this paper, we present a novel Markov Chain Monte Carlo framework for solving global optimization problems in the continuous domain. At each iterate, our algorithm uses a globally reaching Markov kernel to generate a candidate point in the feasible region. This candidate point is then accepted according to a possibly non-reversible acceptance probability. We derive sufficient conditions on t...

Direct-search algorithms form one of the main classes of algorithms for smooth unconstrained derivative-free optimization, due to their simplicity and their well-established convergence results. They proceed by iteratively looking for improvement along some vectors or directions. In the presence of smoothness, first-order global convergence comes from the ability of the vectors to approximate t...