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The linear order complementarity problem. (English) Zbl 0694.90094
Summary: The classical complementarity problem in Euclidean space can be viewed alternatively as a variational inequality or as a lattice orthogonality problem. Generalizations of the former have been extensively studied, but infinite-dimensional analogues of the latter have been largely ignored. Moreover, as we show, many well-known results about the classical complementarity problem are more appropriately viewed order- theoretically. This is particularly true of least element solutions, which are central to the present study of order complementarity in vector lattices. We emphasize that the lattice theoretic descriptions we employ are very useful even in the standard finite-dimensional setting.

MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47H10 Fixed-point theorems
49J40 Variational inequalities
90C48 Programming in abstract spaces
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