College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China; School of Computing, National University of Singapore, Singapore 117417, Singapore.
Key Laboratory of Dependable Services Computing in Cyber-Physical Society (Chongqing) Ministry of Education, College of Computer, Chongqing University, Chongqing 400044, China.
Neural Netw. 2023 Mar;160:259-273. doi: 10.1016/j.neunet.2023.01.012. Epub 2023 Jan 20.
In this paper, a subgradient-based neurodynamic algorithm is presented to solve the nonsmooth nonconvex interval-valued optimization problem with both partial order and linear equality constraints, where the interval-valued objective function is nonconvex, and interval-valued partial order constraint functions are convex. The designed neurodynamic system is constructed by a differential inclusion with upper semicontinuous right-hand side, whose calculation load is reduced by relieving penalty parameters estimation and complex matrix inversion. Based on nonsmooth analysis and the extension theorem of the solution of differential inclusion, it is obtained that the global existence and boundedness of state solution of neurodynamic system, as well as the asymptotic convergence of state solution to the feasible region and the set of LU-critical points of interval-valued nonconvex optimization problem. Several numerical experiments and the applications to emergency supplies distribution and nondeterministic fractional continuous static games are solved to illustrate the applicability of the proposed neurodynamic algorithm.
本文提出了一种基于次梯度的神经动力算法，用于求解具有部分序和线性等式约束的非光滑非凸区间优化问题，其中区间值目标函数是非凸的，区间值偏序约束函数是凸的。所设计的神经动力学系统由一个具有上半连续右手边的微分包含构造，通过减轻罚参数估计和复杂矩阵求逆，可以降低计算负荷。基于非光滑分析和微分包含解的扩展定理，得到了神经动力学系统状态解的全局存在性和有界性，以及状态解渐近收敛到可行区域和区间值非凸优化问题的 LU 关键点集。通过几个数值实验和对紧急物资配送和非确定分数连续静态博弈的应用，说明了所提出的神经动力算法的适用性。
