Modified Fourier-Motzkin Elimination Algorithm for Reducing Systems of Linear Inequalities with Unconstrained Parameters

Current techniques for eliminating redundant inequalities are not viable in higher dimensions. As an alternative we propose a modified version of the Fourier-Motzkin Elimination Algorithm (ModFMEA), implemented in MatLab, to reduce redundancies in a given system of linear constraints over reals posed as linear inequalities. Reduction is obtained, at each orthant containing the solution set, by taking the lower and upper bounds of x_i-normalized inequalities x_i >= l and u >= x_i respectively, where l and u are linear terms with no occurrence of x_i, for i = 1,2,...,N. The reduced system over the whole solution set can be obtained by taking the union of the reduced system at each orthant.