Abstract
The concept of binary relation is applied to generalize the complementarity problem. Dual relations are introduced as an analogue to dual cones in the generalized complementarity problem. A concept of linearization is introduced by considering the minimal linear relation stronger than the given relation. Geometric characteristics are studied as are the interconnections between a binary relation, its linearization and its dual. Existence of solutions for the new type of complementarity problem is investigated. In particular we consider the complementarity problem associated to a relation defined by the union of a family of pointed closed convex cones.
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© 2001 Springer Science+Business Media Dordrecht
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Isac, G., Kostreva, M.M., Polyashuk, M. (2001). Relational Complementarity Problem. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds) From Local to Global Optimization. Nonconvex Optimization and Its Applications, vol 53. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5284-7_15
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DOI: https://doi.org/10.1007/978-1-4757-5284-7_15
Publisher Name: Springer, Boston, MA
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