Model Building and Optimization Analysis of MDF Continuous Hot-Pressing Process by Neural Network

We propose a one-layer neural network for solving a class of constrained optimization problems, which is brought forward from the MDF continuous hot-pressing process. The objective function of the optimization problem is the sum of a nonsmooth convex function and a smooth nonconvex pseudoconvex function, and the feasible set consists of two parts, one is a closed convex subset of Rn, and the other is defined by a class of smooth convex functions. By the theories of smoothing techniques, projection, penalty function, and regularization term, the proposed network is modeled by a differential equation, which can be implemented easily. Without any other condition, we prove the global existence of the solutions of the proposed neural network with any initial point in the closed convex subset. We show that any accumulation point of the solutions of the proposed neural network is not only a feasible point, but also an optimal solution of the considered optimization problem though the objective function is not convex. Numerical experiments on the MDF hot-pressing process including the model building and parameter optimization are tested based on the real data set, which indicate the good performance of the proposed neural network in applications

Convergence analysis of a class of nonsmooth gradient systems

In this paper, we present new results on convergence of a class of nonlinear dynamical systems modeled by the gradients of nonsmooth cost functions. This class of systems arises from neural-network research and can be regarded as a generalization of existing neural-network models. Using the recently developed Lstrokojasiewicz gradient inequality, the convergence analysis of this gradient-like differential inclusion is given. Without assuming the smoothness of the cost function or analyticity of the activation function, we prove the output convergence of the differential system. In addition, for the piecewise analytic activation function with positive first-order derivative, we prove the state convergence. Furthermore, we also discuss the relationship between the convergence rate and the location of terminal limit point. Numerical examples are provided to illustrate the theoretical results and present the goal-seeking capability of the systems