On gap functions for vector variational inequalities. (English) Zbl 0997.49006
Giannessi, Franco (ed.), Vector variational inequalities and vector equilibria. Mathematical theories. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 38, 55-72 (2000).
Summary: We extend the theory of gap functions for scalar variational inequality problems [see A. Auslender: “Optimisation. Méthodes numériques” (1976; Zbl 0326.90057) and F. Giannessi, Ann. Oper. Res. 58, 181-200 (1995; Zbl 0844.90069)] to the case of vector variational inequalities. The gap functions for vector variational inequalities are defined as set-valued mappings. The significance of the gap function is interpreted in terms of the inverse vector variational inequality. Convexity properties of these set-valued mappings are studied under different assumptions.
For the entire collection see [Zbl 0952.00009].
For the entire collection see [Zbl 0952.00009].
MSC:
| 49J40 | Variational inequalities |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
