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Pseudoconvex optimization problem, as an important nonconvex optimization problem, plays an important role in scientific and engineering applications. In this paper, a recurrent one-layer neural network is proposed for solving the pseudoconvex optimization problem with equality and inequality constraints. It is proved that from any initial state, the state of the proposed neural network reaches the feasible region in finite time and stays there thereafter. It is also proved that the state of the proposed neural network is convergent to an optimal solution of the related problem. Compared with the related existing recurrent neural networks for the pseudoconvex optimization problems, the proposed neural network in this paper does not need the penalty parameters and has a better convergence. Meanwhile, the proposed neural network is used to solve three nonsmooth optimization problems, and we make some detailed comparisons with the known related conclusions. In the end, some numerical examples are provided to illustrate the effectiveness of the performance of the proposed neural network.

In this paper, a two-layer recurrent neural network is proposed to solve the nonsmooth convex optimization problem subject to convex inequality and linear equality constraints. Compared with existing neural network models, the proposed neural network has a low model complexity and avoids penalty parameters. It is proved that from any initial point, the state of the proposed neural network reaches the equality feasible region in finite time and stays there thereafter. Moreover, the state is unique if the initial point lies in the equality feasible region. The equilibrium point set of the proposed neural network is proved to be equivalent to the Karush-Kuhn-Tucker optimality set of the original optimization problem. It is further proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov. Moreover, from any initial point, the state is proved to be convergent to an equilibrium point of the proposed neural network. Finally, as applications, the proposed neural network is used to solve nonlinear convex programming with linear constraints and L1 -norm minimization problems.

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