Linear programming in covariant and contravariant manifolds. A physical and mathematical perspective

Abstract

IN THIS PAPER A NEW OPTIMIZATION METHOD IS PRE SENTED. THE THEORETICAL BACK GROUND IS DIFFERENT TO THAT USED PRES ENTLY AS IN THE CASE OF THE ""SIMPLEX METHOD"". THE PRESENTATION IS BASED ON THE USE OF THE COVARIANT AND CONTRAVARIANT SPACES, BOTH BEING BIORTHOGONAL SPACES, AL LOW A VISUALIZATION OF THE OPTIMIZATION PROBLEM FROM A PHYSICAL AS WELL AS MATHEMATICAL POINTS OF VIEW. THE OBTAINED RESULT PRO VIDES THE BEST APPROXIMATION ACCORDING TO THE DATA PROVIDED IN THE CONSTRAINTS OF THE PROBLEM, WHICH ARE VISUALIZED LIKE VECTORS AND NOT LIKE STRAIGHT LINES, PLANES OR HYPERPLANES. ALSO, IN THIS NEW METHOD THE ERROR GENERATED BETWEEN THE APPROXIMATION AND THE OBJECTIVE VECTORS CAN BE MEASURED, WHICH ALLOWS TO OBSERVE AND PROVE THE ACCURACY OF THE PROPOSED SOLUTION.