Higher-order interior point methods for convex nonlinear programming

Abstract

This paper extends the concept of higher-order search directions within interior point methods to convex nonlinear programming. This includes the mathematical framework needed to compute the higher-order derivatives. The paper also highlights some special cases where the computation of these higher-order derivatives is simplified and a dimensional lifting procedure for transforming a large number of general nonlinear problems into one of these more efficient forms. The paper further describes the algorithmic development required to employ these higher-order search directions in a practical algorithm. Computational results are presented for a large number of test problems, highlighting higher-order methods’ strong potential for decreasing iteration count and their case-by-case potential for decreasing CPU time.