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Strong uniqueness in sequential linear programming

Published online by Cambridge University Press:  17 February 2009

M. R. Osborne  and
R. S. Womersley
M. R. Osborne
Affiliation:
Statistics Research Section, Mathematical Sciences School, Australian National University, Canberra, A.C.T. 2601, Australia.
R. S. Womersley
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 4 , April 1990 , pp. 379 - 384
Copyright
Copyright © Australian Mathematical Society 1990

References

[1] Cromme, L., “Strong uniqueness. A far reaching criterion for the convergence analysis of iterative procedures,” Numer. Math. 29 (1978) 179–193.CrossRefGoogle Scholar
[2] Jittorntrum, K. and Osborne, M. R., “Strong uniqueness and second order convergence in nonlinear discrete approximation,” Numer. Math. 34 (1980) 439–455.CrossRefGoogle Scholar
[3] Womersley, R. S., “Local properties of algorithms for minimizing nonsmooth composite functions,” Math. Prog. 32 (1985) 69–89.CrossRefGoogle Scholar
[4] Wright, Stephen, “Convergence of SQP- like methods for constrained optimization,” SIAM J. Cont. and Optim. (to appear).Google Scholar
[5] Zhang, Jianzhong, Kim, Nae-heon, and Lasdon, L., “An improved successive linear programming algorithm,” Manag. Sci. 31 (1985) 1312–1331.CrossRefGoogle Scholar