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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

MSC:
49J40Variational methods including variational inequalities
90C29Multi-objective programming; goal programming
90C47Minimax problems
47J20Inequalities involving nonlinear operators
References:
[1] · Zbl 0988.49004 · doi:10.1023/A:1017581009670
[2]
[3]Chen G.-Y., Goh C.J., Yang X.Q. (2000). On gap functions for vector variational inequalities, in [4], 55–72.
[4]
[5] · Zbl 1009.90093 · doi:10.1016/S0377-2217(98)00047-2
[6]
[7]
[8]
[9]
[10]
[11]
[12] · Zbl 0892.90158 · doi:10.1023/A:1022647607947