Department of Mathematics, Harbin Institute of Technology, Weihai, China.
School of Economics and Management, Harbin Institute of Technology, Harbin, China.
Neural Netw. 2024 Aug;176:106337. doi: 10.1016/j.neunet.2024.106337. Epub 2024 Apr 26.
The complex and diverse practical background drives this paper to explore a new neurodynamic approach (NA) to solve nonsmooth interval-valued optimization problems (IVOPs) constrained by interval partial order and more general sets. On the one hand, to deal with the uncertainty of interval-valued information, the LU-optimality condition of IVOPs is established through a deterministic form. On the other hand, according to the penalty method and adaptive controller, the interval partial order constraint and set constraint are punished by one adaptive parameter, which is a key enabler for the feasibility of states while having a lower solution space dimension and avoiding estimating exact penalty parameters. Through nonsmooth analysis and Lyapunov theory, the proposed adaptive penalty-based neurodynamic approach (APNA) is proven to converge to an LU-solution of the considered IVOPs. Finally, the feasibility of the proposed APNA is illustrated by numerical simulations and an investment decision-making problem.
复杂多样的实际背景促使本文探索一种新的神经动力学方法（NA）来解决由区间偏序和更一般的集合约束的非光滑区间值优化问题（IVOPs）。一方面，为了处理区间值信息的不确定性，通过确定性形式建立了 IVOPs 的 LU 最优性条件。另一方面，根据罚方法和自适应控制器，通过一个自适应参数来惩罚区间偏序约束和集合约束，这是状态可行性的关键因素，同时具有更低的解空间维度，并避免估计精确的罚参数。通过非光滑分析和 Lyapunov 理论，证明了所提出的基于自适应罚的神经动力学方法（APNA）收敛到所考虑的 IVOPs 的 LU 解。最后，通过数值模拟和投资决策问题说明了所提出的 APNA 的可行性。
