协同神经动力学优化求解非线性方程。
Collaborative neurodynamic optimization for solving nonlinear equations.
机构信息
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China.
Key Laboratory of Intelligent Education Technology and Application of Zhejiang Province, Zhejiang Normal University, Jinhua 321004, China; School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China; School of Automation and Electrical Engineering, Linyi University, Linyi 276005, China.
出版信息
Neural Netw. 2023 Aug;165:483-490. doi: 10.1016/j.neunet.2023.05.054. Epub 2023 Jun 7.
A distributed optimization method for solving nonlinear equations with constraints is developed in this paper. The multiple constrained nonlinear equations are converted into an optimization problem and we solve it in a distributed manner. Due to the possible presence of nonconvexity, the converted optimization problem might be a nonconvex optimization problem. To this end, we propose a multi-agent system based on an augmented Lagrangian function and prove that it converges to a locally optimal solution to an optimization problem in the presence of nonconvexity. In addition, a collaborative neurodynamic optimization method is adopted to obtain a globally optimal solution. Three numerical examples are elaborated to illustrate the effectiveness of the main results.
本文提出了一种求解带约束非线性方程组的分布式优化方法。将多个约束非线性方程组转化为优化问题，并以分布式的方式求解。由于可能存在非凸性，转换后的优化问题可能是一个非凸优化问题。为此，我们提出了一种基于增广拉格朗日函数的多智能体系统，并证明在非凸性存在的情况下，它能够收敛到优化问题的局部最优解。此外，还采用了协同神经动力学优化方法来获得全局最优解。通过三个数值实例来说明主要结果的有效性。
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