Higher-order derivatives in linear and quadratic programming

Abstract

An interior method for linear and quadratic programming which makes use of higher derivatives of the logarithm barrier function is presented. A convergence analysis is considered too. Our computational experience shows that the method considered performs quite well and seems to be more reliable and robust than the standard method. Scope and purpose Linear programming problems were, for many years, the exclusive domain of the simplex algorithm developed by G.B. Dantzing in 1947. With the introduction of a new algorithm, developed by N.K. Karmarkar in 1984, an alternative computational approach became available for solving such problems. This algorithm established a new class of algorithms: interior point methods for linear programming. In this paper we introduce a barrier method for solving a linear and quadratic programming problem which [9–15] makes use of higher-order derivatives. We note that a different approach used to construct higher-order interior point methods is presented in [1–4]. We think that making use of an approximation of higher-order we may obtain a faster convergence and an algorithm more robust than a method obtained using a second-order approximation.