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**Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequalities.**
*(English)*
Zbl 1067.49007

Summary: The auxiliary principle technique is extended to study the generalized strongly nonlinear mixed variational-like inequality problem for set-valued mappings without compact values. We establish first the existence of a solution of the related auxiliary problem. Then, the iterative algorithm for solving that problem is given by using this existence result. Moreover, the existence of a solution of the original problem and the convergence of iterative sequences generated by the algorithm are both derived.

### Keywords:

mixed variational-like inequalities; auxiliary principle technique; iterative algorithms; existence theorems; set-valued mappings
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\textit{L. C. Zeng} et al., J. Optim. Theory Appl. 124, No. 3, 725--738 (2005; Zbl 1067.49007)

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