On Interior-Point Methods, Related Dynamical Systems Results and Cores of Targets for Linear Programming

Abstract

This article examined interior-point methods for solving linear programming problems. Then it collected key relevant results, formulated analogous continuous dynamical systems, pioneered the introduction of cores of targets concept and established a sequence of lemmas which would be 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 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.