A neurodynamic approach to convex optimization problems with general constraint

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• 作者：Sitian Qin^a ; ^{qinsitian@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yadong Liu^a ; ^{hitliuyadong1994@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xiaoping Xue^b ; ^{xiaopingxue@263.net" class="auth_mail" title="E-mail the corresponding author} ; Fuqiang Wang^c
• 关键词：Nonsmooth convex optimization ; Neurodynamic approach ; Łojasiewicz inequality ; Convergence in finite time
• 刊名：Neural Networks
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：84
• 期：Complete
• 页码：113-124
• 全文大小：738 K

文摘

This paper presents a neurodynamic approach with a recurrent neural network for solving convex optimization problems with general constraint. It is proved that for any initial point, the state of the proposed neural network reaches the constraint set in finite time, and converges to an optimal solution of the convex optimization problem finally. In contrast to the existing related neural networks, the convergence rate of the state of the proposed neural network can be calculated quantitatively via the Łojasiewicz exponent under some mild assumptions. As applications, we estimate explicitly some Łojasiewicz exponents to show the convergence rate of the state of the proposed neural network for solving convex quadratic optimization problems. And some numerical examples are given to demonstrate the effectiveness of the proposed neural network.