IEEE Trans Neural Netw Learn Syst - A two-layer recurrent neural network for nonsmooth convex optimization problems.

Tópicos

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Resumo

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.

Resumo Limpo

paper twolay recurr neural network propos solv nonsmooth convex optim problem subject convex inequ linear equal constraint compar exist neural network model propos neural network low model complex avoid penalti paramet prove initi point state propos neural network reach equal feasibl region finit time stay thereaft moreov state uniqu initi point lie equal feasibl region equilibrium point set propos neural network prove equival karushkuhntuck optim set origin optim problem prove equilibrium point propos neural network stabl sens lyapunov moreov initi point state prove converg equilibrium point propos neural network final applic propos neural network use solv nonlinear convex program linear constraint l norm minim problem

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