On Convergence Conditions of an Extended Projection Neural Network

Abstract

The output trajectory convergence of an extended projection neural network was developed under the positive definiteness condition of the Jacobian matrix of nonlinear mapping. This note offers several new convergence results. The state trajectory convergence and the output trajectory convergence of the extended projection neural network are obtained under the positive semidefiniteness condition of the Jacobian matrix. Comparison and illustrative examples demonstrate applied significance of these new results.

A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem

“…Then, we compare the structural complexities of the four -WTA networks (15), (16), (18), and (21). Because all of them are of complexity, it is necessary to give a more accurate estimation of the number of elements in them.…”

“…In this section, we use several numerical examples to illustrate the performances of proposed neural networks (9) and (21). The simulations are conducted in MATLAB.…”

“…The solution found in this run is . Example 3: Let us solve a -WTA problem with network (21). The problem is taken from [40], which was designed to test the performance of (15).…”

“…When coincides with , and is within approximately , where either of them can be regarded as the second largest element, the -WTA network (16) cannot be applied here. We use network (21) with to accomplish the task and the outputs are recorded in the other four graphs of Fig. 8.…”

Neurodynamic Optimization: towards Nonconvexity

“…In a series of papers (Xia & Wang, 2004;Xia, 2004;Xia & Feng, 2005;, a recurrent neural network, termed extended projection neural network (or EPNN for short), was developed for solving the convex optimization problems in the form of (7) with the following dynamical equation:…”