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.
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。
