A MODIFIED SIMPLEX METHOD FOR SOLVING 1-NORM MINIMIZATION PROBLEM IN MODEL PREDICTIVE CONTROL

摘要

Since the simplex method requires the polyhedron to be in the positive domain,the 1 -norm minimization problems are formulated by substantially increasing the size of the LP problems.This paper presents a simple modification that enables the simplex method to be directly applicable to a polyhedron,which extends into the negative domain.That is,instead of requiring the problem to change,the method is changed to fit the problem.The modification eliminates the need to increase the size of the problem and thus eliminates the associated computational effort.The proposed method skips iterations and Phase 1 of the simplex method.Its computational advantage is verified in two examples.