Convergence Behaviour of Some Iteration Procedures for Exterior Point Method of Centres Algorithms

摘要

The convergence rate for a number of iterative procedures for the method of centres, was studied in connection with the investigation of methods for extending the applicability of flight directors. By the use of the Kuhn-Tucker conditions and the duality properties for convex programming problems, it was shown that the augmented cost function, arising in this method, has a second order zero at the optimum point. From this flows the results: that the Staha and Morrison iteration procedures are linearly convergent; the tangent iteration procedure is quadratically convergent; and two interpolation polynomial iteration procedures proposed by the author to overcome the deficiencies of the tangent method away from the optimum point are super-linearly convergent and are thus worthy of further investigation. (Author)