Moore-Penrose pseudo-inverse matrix and generalized dual variables in mathematical programming

This paper extends the definition and usage of dual variables as well as the sensitivity of the parameters of a linear or a non-linear mathematical program at any point within the feasible set. This extension is of major importance as it provides information beyond that available from either the extreme points of the feasible set or the optimal solution point. The theoretical basis of the proposed approach is proven and numerical examples are provided illustrating its applicability as an analytical tool.