A logarithm barrier method for linear programming

Abstract

In a previous paper [6] we introduce an algorithm for solving an unconstrained optimization problem based on an iterative process which makes use of higher order derivatives. In this paper we consider the iterative process presented in [6] and prove the cubic convergence of this process. We, moreover, introduce an interior point method for solving a linear programming problem making use of a Taylor series expansion related to the gradient of the penalty function. Finally some numerical results are reported.

Keywords:

• Barrier method
• cubic convergence
• linear programming

C.R. Category:

• G.1.6