The Generalized Inverse in Linear Programming Basic Theory
نویسنده
چکیده
Properties of the (Moore-Penrose-Bjerharamar) generalised inverse A of an arbitrary m by n matrix A are presented and utilized in formulating a linear programming problem, in terms of the eigenvectors of I A + A, which is equivalent to the direct (equalities) form of the linear programming problem. The duality theorem of linear programming is considered from the point of view of this reformulation and a characterization of duality in terms of orthogonality is derived. Other properties of the reformulation are used to characterize edgea and extreme points of the convex set of feasible solutions in terms of eigenvectors of certain projection matrices.
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تاریخ انتشار 2018