IEEE Trans Neural Netw Learn Syst. 2018 May;29(5):1562-1574. doi: 10.1109/TNNLS.2017.2676046. Epub 2017 Mar 16.
In this paper, a neural network model for solving a class of multiextremal smooth nonconvex constrained optimization problems is proposed. Neural network is designed in such a way that its equilibrium points coincide with the local and global optimal solutions of the corresponding optimization problem. Based on the suitable underestimators for the Lagrangian of the problem, one give geometric criteria for an equilibrium point to be a global minimizer of multiextremal constrained optimization problem with or without bounds on the variables. Both necessary and sufficient global optimality conditions for a class of multiextremal constrained optimization problems are presented to determine a global optimal solution. By study of the resulting dynamic system, it is shown that under given assumptions, steady states of the dynamic system are stable and trajectories of the proposed model converge to the local and global optimal solutions of the problem. Numerical results are given and related graphs are depicted to illustrate the global convergence and performance of the solver for multiextremal constrained optimization problems.
本文提出了一种用于求解一类多极值光滑非凸约束优化问题的神经网络模型。神经网络的设计方式使得其平衡点与相应优化问题的局部和全局最优解一致。基于问题的拉格朗日的合适估计器，给出了在变量有界或无界的情况下，平衡点是多极值约束优化问题的全局极小值的几何准则。给出了一类多极值约束优化问题的充分必要全局最优性条件，以确定全局最优解。通过对所得动力系统的研究，证明了在所给假设下，动力系统的稳态是稳定的，并且所提出模型的轨迹收敛于问题的局部和全局最优解。给出了数值结果，并绘制了相关图形，以说明求解多极值约束优化问题的求解器的全局收敛性和性能。
