A new recurrent neural network for solving convex nonlinear programming problems is presented. The new neural network model is described by the following nonlinear dynamical system: \[ {dx\over dt}=-\nabla f(x)+y\nabla g(x),\qquad {dy\over dt}= -g(x),\;y\leq 0,\tag{1} \] where \(f(x)\), \(g_i(x): \mathbb{R}^n\to \mathbb{R}^1\), \(x\in \mathbb{R}^n\), the functions \(f(x)\) and \(g_j(x)\), \(j= 1,2,\dots,m\) are differentiable and convex.
Main result: If the neural network whose dynamics is described by the nonlinear differential equations (1) converges to a stable state \(x(.)\) and \(y(.)\), then the state \(x(.)\) is the optimal solution of the problem: \[ \text{minimize }f(x)\text{ subject to }g(x)= [g_1(x),\dots,g_m(x)]\leq 0. \] The authors show that the neural network has a good stability.
Finally, several examples to demonstrate the behaviour of proposed neural network model are given.