Research On Nonsmooth Neurodynamic Pseudoconvex Optimization Problems

As parallel computation models with fast convergence, neural networks are widely applied in a variety of optimization problems. However, most of the neuro-dynamic optimization problems are convex, and few researches concerned with nonconvex optimization problems are reported. Pseudoconvex optimization pro-blem, as an important nonconvex optimization problem, is widely applied into real life. Based on the neural network theory, in this paper, two different neural networks will be proposed to solve nonsmooth pseudoconvex optimization problems.The first proposed neural network in this paper for nonsmooth pseudoconvex optimization problems, does not depend on the penalty parameter and has a simple structure. It is proved that from any initial point, t he state of the proposed neural network reaches the feasible region in finite time and stays there thereafter. The state of the proposed neural network is convergent to an optimal solution of pseudoconvex optimization problems. Compared with the related existing recurrent neural networks for the pseudoconvex optimization problems, the first prop osed neural network in this paper does not need the penalty parameters and has a better convergence. In addition, the proposed neural network is used to solve three nonsmooth optimization problems, and we make some detailed comparisons with the known related conclusions.Although the above proposed neural network does not depend on the penalty parameters, some additional assumptions are introduced to guarantee the converg-ence. To overcome the shortcoming, by introducing appropriate penalty parameters, we propose another neural network to solve the nonsmooth pseudoconvex optimi-zation problems. At the same time, under the more general assumptions, we prove that from any initial point, the state of the second proposed neural network reaches the feasible region in finite time and finally converges to an optimal solution of the pseudoconvex optimization problems.