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A scalarization approach for vector variational inequalities with applications. (English) Zbl 1097.49014
Summary: We consider an approach to convert vector variational inequalities into an equivalent scalar variational inequality problem with a set-valued cost mapping. Being based on this property, we give an equivalence result between weak and strong solutions of set-valued vector variational inequalities and suggest a new gap function for vector variational inequalities. Additional examples of applications in vector optimization, vector network equilibrium and vector migration equilibrium problems are also given

49J40Variational methods including variational inequalities
90C29Multi-objective programming; goal programming
90C47Minimax problems
47J20Inequalities involving nonlinear operators
Full Text: DOI
[1] · Zbl 0988.49004 · doi:10.1023/A:1017581009670
[3] Chen G.-Y., Goh C.J., Yang X.Q. (2000). On gap functions for vector variational inequalities, in [4], 55--72. · Zbl 0997.49006
[5] · Zbl 1009.90093 · doi:10.1016/S0377-2217(98)00047-2
[12] · Zbl 0892.90158 · doi:10.1023/A:1022647607947