On Linear Inequality Systems without Strongly Redundant Constraints

For an (m x n)-matrix A the set C(A) is studied containing the constraint vectors b of R(m) without strongly redundant inequalities in the system (Ax less-than-or-equal-to b, x greater-than-or-equal-to 0). C(A) is a polyhedral cone containing as a subset the cone Col(A) generated by the column vectors of A. This paper characterizes the matrices A for which the equality C(A) = Col(A) holds. Furthermore, the matrices A are characterized for which C(A) is generated by those constraint vectors beta(i) is-an-element-of C(A), i is-an-element-of {1, 2, ..., m}, for which the feasible region {x is-an-element-of R+n: Ax less-than-or-equal-to beta(i)} equals {x is-an-element-of R+n: (Ax)i less-than-or-equal-to 1}. Necessary conditions are formulated for a constraint vector to be an element of C(A). The class of matrices is characterized for which these conditions are also sufficient.