On Path-Following Dynamical Systems Trajectories for Linear Optimization Problems in Standard Form

Abstract

This article examined path-following methods for solving linear programming problems. Then it collected key relevant results in Ukwu [1], formulated analogous continuous dynamical systems, and established a sequence of propositions which were invoked to prove that the system’s trajectories converge to the optimal solution of a linear programming problem in standard form, under appropriate conditions. These results were made possible by the exploitation of norm properties, their derivatives and the theory of ordinary differential equations, paving the way for the pursuits of satisfying solutions of some linear optimization problems that may not require exact optimal solutions but particular solutions at specified tolerance levels, within feasible guidelines or constraints