Convergence analysis of projection methods for a new system of general nonconvex variational inequalities.

*(English)*Zbl 06214014Summary: In this article, we introduce and consider a new system of general nonconvex variational inequalities defined on uniformly prox-regular sets. We establish the equivalence between the new system of general nonconvex variational inequalities and the fixed point problems to analyze an explicit projection method for solving this system. We also consider the convergence of the projection method under some suitable conditions. Results presented in this article improve and extend the previously known results for the variational inequalities and related optimization problems.

##### MSC:

47J20 | Variational and other types of inequalities involving nonlinear operators (general) |

47N10 | Applications of operator theory in optimization, convex analysis, mathematical programming, economics |

49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |

##### Keywords:

system of general nonconvex variational inequalities; explicit projection methods; uniform prox-regular set; \(r\)-strongly monotone mappings; \(\mu\)-Lipschitz continuous
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\textit{D.-J. Wen} et al., Fixed Point Theory Appl. 2012, Paper No. 59, 10 p. (2012; Zbl 06214014)

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##### References:

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