ISSN:
1436-4646
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract For a fixedm × n matrixA, we consider the family of polyhedral setsX b ={x|Ax ≥ b}, b ∈ R m , and prove a theorem characterizing, in terms ofA, the circumstances under which every nonemptyX b has a least element. In the special case whereA contains all the rows of ann × n identity matrix, the conditions are equivalent toA T being Leontief. Among the corollaries of our theorem, we show the linear complementarity problem always has a unique solution which is at the same time a least element of the corresponding polyhedron if and only if its matrix is square, Leontief, and has positive diagonals.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01584992
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