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A modified barrier function method with improved rate of convergence for degenerate problems

Published online by Cambridge University Press:  17 February 2009

Krisorn Jittorntrum  and
M. R. Osborne
Krisorn Jittorntrum
Affiliation:
Department of Mathematics, Chiengmai University, Cheingmai, Thailand
M. R. Osborne
Affiliation:
Department of Statistics, Institute of Advanced Studies, Australian National University, Canberra, A.C.T. 2600
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Abstract

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In a previous paper the authors have shown that the classical barrier function has an O(r) rate of convergence unless the problem is degenerate when it reduces O(r½). In this paper a modified barrier function algorithm is suggested which does not suffer from this problem. It turns out to have superior scaling properties which make it preferable to the classical algorithm, even in the nondegenerate case, if extrapolation is to be used to accelerate convergence.

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 3 , January 1980 , pp. 305 - 329
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Fiacco, A. V. and McCormick, O. P., Nonlinear programming: sequential unconstrained minimization techniques (Wiley, 1968).Google Scholar
[2]Jittorntrum, K., “Sequential algorithms in nonlinear programming”, (Ph.D. thesis, Australian National University, 1978).CrossRefGoogle Scholar
[3]Jittorntrum, K., “Accelerated convergence for the Powell/Hestenes multiplier method”, Math. Programming (1979) (to appear).CrossRefGoogle Scholar
[4]Jittorntrum, K. and Osborne, M. R., “Trajectory analysis and extrapolation in barrier function methods”, J. Austral. Math. Soc. B 21 (1978), 1–18.Google Scholar
[5]Laurent, P. J., “Convergence de procédé d'extrapolation de Richardson”, Troisième Congrès de l'AFCALTI (Toulouse, 1963), 81–98.Google Scholar
[6]Osborne, M. R., “Topics in optimization” (Comp. Sci. Dept., Stanford University, STAN-CS–72–279).Google Scholar
[7]Powell, M. J. D., “A fast algorithm for nonlinearly constrained optimization calculations”, in Numerical analysis (Lecture notes in mathematics No. 630, New York: Springer-Verlag, 1978), 144–157.CrossRefGoogle Scholar