Adaptive penalty-based neurodynamic approach for nonsmooth interval-valued optimization problem.

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.

A continuous-time neurodynamic approach and its discretization for distributed convex optimization over multi-agent systems.

Distributed optimization problem (DOP) over multi-agent systems, which can be described by minimizing the sum of agents' local objective functions, has recently attracted widespread attention owing to its applications in diverse domains. In this paper, inspired by penalty method and subgradient descent method, a continuous-time neurodynamic approach is proposed for solving a DOP with inequality and set constraints. The state of continuous-time neurodynamic approach exists globally and converges to an optimal solution of the considered DOP.

A One-Layer Recurrent Neural Network for Constrained Complex-Variable Convex Optimization.

In this paper, based on calculus and penalty method, a one-layer recurrent neural network is proposed for solving constrained complex-variable convex optimization. It is proved that for any initial point from a given domain, the state of the proposed neural network reaches the feasible region in finite time and converges to an optimal solution of the constrained complex-variable convex optimization finally. In contrast to existing neural networks for complex-variable convex optimization, the proposed neural network has a lower model complexity and better convergence.