we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems a...

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems are giv...

In this paper, we discuss dynamics of Cohen–Grossberg neural networks with discontinuous activations functions. We provide a relax set of sufficient conditions based on the concept of Lyapunov diagonally stability (LDS) for Cohen–Grossberg networks to be absolutely stable. Moreover, under certain conditions we prove that the system is exponentially stable globally or convergent globally in fini...

Recently, based upon the Chen-Harker-Kanzow-Smale smoothing function and the trajectory and the neighbourhood techniques, Hotta and Yoshise proposed a non-interior point algorithm for solving the nonlinear com-plementarity problem. Their algorithm is globally convergent under a relatively mild condition. In this paper, we modify their algorithm and combine it with the superlinear convergence th...

Recently, based upon the Chen-Harker-Kanzow-Smale smoothing function and the trajectory and the neighbourhood techniques, Hotta and Yoshise proposed a noninterior point algorithm for solving the nonlinear complementarity problem. Their algorithm is globally convergent under a relatively mild condition. In this paper, we modify their algorithm and combine it with the superlinear convergence theo...

Coherent x-ray diffractive imaging is a novel imaging technique that utilizes phase retrieval and nonlinear optimization methods to image matter at nanometer scales. We explore how the convergence properties of a popular phase retrieval algorithm, Fienup’s HIO, behave by introducing a reduced dimensionality problem allowing us to visualize and quantify convergence to local minima and the global...

In this paper a globally convergent first–order training algorithm is proposed that uses sign–based information of the batch error measure in the framework of the nonlinear Jacobi process. This approach allows us to equip the recently proposed Jacobi–Rprop method with the global convergence property, i.e. convergence to a local minimiser from any initial starting point. We also propose a strate...