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An Ekeland’s variational principle for set-valued mappings with applications. (English) Zbl 1165.49021
Summary: We obtain a general Ekeland’s variational principle for set-valued mappings in complete metric space, which is different from those in [G. Y. Chen and X. X. Huang, Math. Methods Oper. Res. 48, No. 2, 181–186 (1998; Zbl 0936.49012); G. Y. Chen, X. X. Huang and S. H. Hou, J. Optimization Theory Appl. 106, No. 1, 151–164 (2000; Zbl 1042.90036); S.-J. Li and W.-Y. Zhang, Acta Math. Appl. Sin., Engl. Ser. 23, No. 1, 141–148 (2007; Zbl 1112.49018)]. By the result, we prove some existence results for a general vector equilibrium problem under nonconvex and compact or noncompact assumptions of its domain, respectively. Moreover, we give some equivalent results to the variational principle.
49J53Set-valued and variational analysis
49J52Nonsmooth analysis (other weak concepts of optimality)
49J45Optimal control problems involving semicontinuity and convergence; relaxation