Generalized-Hukuhara Subgradient-Based Neurodynamic Approach to Nonsmooth Constrained Distributed Interval-Valued Optimization

In this paper, we propose a projection-type neuro-dynamic approach for solving a class of nonsmooth constrained distributed optimization problems with interval-valued local objective functions over a network of vertices. We introduce the concept of generalized-Hukuhara subgradient (gH-subgradient) and differential inclusion system in the algorithm framework, aiming to cope with the confusion that objective functions may not be gH-differentiable, and further deriving the efficiency condition of the solution of the problem by empolying the geometry relationship between the gH-subgradient and the normal cone. The boundedness and convergence of the state solution of the proposed neurodynamic algorithm are provable, and the conclusion that the state outputs of all vertices reach consensus on the efficient solution of the problem can be guaranteed by Lyapunov function method and Byrnes-Martin integral invariant principle. The designed neurodynamic model is simple in structure, avoids the calculation of matrix inversion and the introduction of Lagrange multipliers, and is suitable for solving general distributed optimization problems with interval-valued functions and constraints. Finally, the simulation applications of network utility, power flow balancing and gas transportation show the viability of the proposed algorithm.