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On the solution of a partially structured nonlinear program

Published online by Cambridge University Press:  17 February 2009

P. D. Simms
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, S.A. 5000
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Abstract

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A class of partially structured nonlinear programming problems, containing the capacitated nonlinear minimum cost multicommodity flow problem, is considered. Such problems, although large, can often be solved efficiently and with minimal computational storage by gradient projection methods.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Berry, L. T. M., “On the solution of a structured non-linear programme”, J. Austral. Math. Soc. Ser. B 19 (1975), 242248.CrossRefGoogle Scholar
[2]Berry, L. T. M., A mathematical model for optimizing telephone networks (Ph.D. thesis, University of Adelaide, 1971).Google Scholar
[3]Bjorck, A., “Comment on the iterative refinement of least-squares solutions”, J. American Stat. Assoc. 73, 361 (1978), 161166.Google Scholar
[4]Boullion, T. L. and Odell, P. L., Generalized inverse matrices (Wiley-Interscience, 1971).Google Scholar
[5]Fletcher, R., “A technique for orthogonalisation”, J. Inst. Maths Applics 5 (1969), 162166.Google Scholar
[6]Gill, P. E., Golub, G. H., Murray, W. and Saunders, M. A., “Methods for modifying matrix factorization”, Math, of Comp. 28 (1974), 505535.Google Scholar
[7]Gill, P. E. and Murray, W., “Modification of matrix factorization after a rank one change”, in The state of the art in numerical analysis (ed. Jacobs, D.) (Academic Press, 1976).Google Scholar
[8]Gill, P. E. and Murray, W., “Numerically stable methods for quadratic programming”, Math. Programming 14 (1978), 349372.CrossRefGoogle Scholar
[9]Goldfarb, D., “Extension of Davidon's variable metric method to maximization under linear inequality and equality constraints”, SIAM J. Appl. Math. 17 (1969), 739764.CrossRefGoogle Scholar
[10]Golub, G. H. and Wilkinson, J. H., “Note on the iterative refinement of least squares solutions”, Numerische Mathematik 9 (1966), 139148.Google Scholar
[11]Rosen, J. B., “The gradient projection method for nonlinear programming. Part I. Linear constraints”, SIAM J. Appl. Math. 8 (1960), 181217.Google Scholar
[12]Shah, B. V., Buehler, R. J. and Kempthorne, O., “Some algorithms for minimizing a function of several variables”, SIAM J. Appl. Math. 12 (1964), 7492.Google Scholar