Generic well posedness in linear programming

Description

We consider the following pair of linear programming problems in duality: parameterized by the m × n matrix A defining the inequality constraints. The main result of the paper states that in the case m ≥ n the set S of well posed problems in a very strong sense is a generic subset of the set of problems having solution. Generic here means that S is an open and dense set whose complement is contained in a finite union of algebraic surfaces of dimension less than mn. © 2008 Yokohama Publishers.

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