Abstract
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.
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Research partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai, China. Research partially supported by a grant from the National Science Council of Taiwan
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Zeng, L.C., Schaible, S. & Yao, J.C. Iterative Algorithm for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities. J Optim Theory Appl 124, 725–738 (2005). https://doi.org/10.1007/s10957-004-1182-z
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DOI: https://doi.org/10.1007/s10957-004-1182-z