A General Projection Neural Network for Solving Monotone Variational Inequalities and Related Optimization Problems

Abstract

Recently, a projection neural network for solving monotone variational inequalities and constrained optimization problems was developed. In this paper, we propose a general projection neural network for solving a wider class of variational inequalities and related optimization problems. In addition to its simple structure and low complexity, the proposed neural network includes existing neural networks for optimization, such as the projection neural network, the primal-dual neural network, and the dual neural network, as special cases. Under various mild conditions, the proposed general projection neural network is shown to be globally convergent, globally asymptotically stable, and globally exponentially stable. Furthermore, several improved stability criteria on two special cases of the general projection neural network are obtained under weaker conditions. Simulation results demonstrate the effectiveness and characteristics of the proposed neural network.

Motion planning with obstacle avoidance for kinematically redundant manipulators based on two recurrent neural networks

“…Because Q is positive semidefinite only and many neural networks including the SDNN used in [3] can not be applied. But according to [18], this problem can be formulated into an equivalent generalized linear variational inequality, and as a consequence, it can be solved by the general projection neural network (GPNN) studied extensively in [14], [15], [19]. When specialized to solve (1) the GPNN's dynamic equation is as follows (cf.…”

“…In this paper, an even simpler neural network, the improved dual neural network (IDNN) reported in [14] is applied for solving the problem. Since neither SDNN nor IDNN can solve the critical point problem which is not strictly convex, a general projection neural network (GPNN) [15] is applied.…”

Three Global Exponential Convergence Results of the GPNN for Solving Generalized Linear Variational Inequalities

“…Consider the function V (u(t)) = u(t) − u * 2 /2 where u * is a finite equilibrium point of (14). Following a similar analysis procedure to that of Corollary 4 in [5] we can derive…”

“…where x and x are constants (without loss of generality, any component of x or −x can be −∞), a neurodyamic approach was proposed in [4] and [5] from different viewpoints for solving it. Moreover, in [5], the neurodynamic system was given a name, general projection neural network (GPNN).…”

“…Moreover, in [5], the neurodynamic system was given a name, general projection neural network (GPNN). A general form of the system is as follows:…”