A One-Layer Recurrent Neural Network for Pseudoconvex Optimization Problems With Equality and Inequality Constraints
提出一种单层递归神经网络，用于求解带等式和不等式约束的伪凸优化问题，无需惩罚参数且收敛性更好，并通过数值例子验证了有效性。
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.