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An operator splitting method for variational inequalities with partially unknown mappings. (English) Zbl 1159.65069

Authors’ summary: We propose a new operator splitting method for solving a class of variational inequality problems in which part of the underlying mappings are unknown. This class of problems arises frequently from engineering, economics and transportation equilibrium problems. At each iteration, by using the information observed from the system, the method solves a system of nonlinear equations, which is well-defined. Under mild assumptions, the global convergence of the method is proved, and its efficiency is demonstrated with numerical examples.

MSC:

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M25 Discrete approximations in optimal control
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