Obtaining simultaneous solutions of linear subsystems of inequalities and duals Original Research Article

Given a set S of linear relations (equations and/or inequalities) among n variables, the problem of solving the systems resulting after selecting any subsets of S is dealt with. An algorithm that obtains all the necessary information to solve this problem, even if the operator in each linear relation is chosen, at wish, as an equality or inequality less-than-or-equals, slant,<,greater-or-equal, slanted, or > is given. In addition, this algorithm simultaneously obtains the orthogonal set (dual cone) of a linear space (cone) generated by any subset of a given set of vectors (including sign selection), and allows simplifying the representation of the resulting linear spaces and cones to their minimal representations. The proposed methods are illustrated with several examples.