J Austral Math Soc Ser B 31 pp379--384, 1990.

Strong uniqueness in sequential linear programming

M. R. Osborne and R. S. Womersley

Abstract

It is known that strong uniqueness can be used to prove second order convergence of the generalised Gauss-Newton algorithm. Formally this algorithm includes sequential linear programming as a special case. Here we show that the second order convergence result extends when the sequential linear programming algorithm is formulated appropriately. Also this discussion provides an example which shows that the assumption of Lipschitz continuity is necessary for the second order convergence result based on strong uniqueness.

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Authors

M. R. Osborne

Statistics Research Section, Mathematical Sciences School, Australian National University, Canberra, A.C.T. 2601, Australia.

R. S. Womersley

School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia.