Notes on a neural network approach to inverse variational inequalities. (English) Zbl 1518.49013
Summary: We consider a neural network approach to an inverse variational inequality which is assumed to have a non-empty set of solutions. In the case of gradient mappings, we prove that every trajectory of the network converges to the solution set in the case of convex potentials and if the solution set is singleton, the network is globally asymptotically stable at the equilibrium point. We also prove that if the network has a strongly convex potential, then the network is globally exponentially stable at the equilibrium point. Another purpose of this paper is to point out certain fatal mistakes in the paper by X. Zou et al. [Neurocomputing 173, Part 3, 1163–1168 (2016; doi:10.1016/j.neucom.2015.08.073)].
MSC:
| 49J40 | Variational inequalities |
| 65K15 | Numerical methods for variational inequalities and related problems |
Keywords:
neural network; inverse variational inequality; convergence; global stability; projection; monotone mappingReferences:
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