A new low-rank quasi-Newton update scheme for nonlinear programming

R. Fletcher

    Research output: Chapter in Book/Report/Conference proceedingChapter

    4 Citations (Scopus)

    Abstract

    A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden family, although invariance under linear transformations of the variables is preserved. The representation provides a limited memory capability, and there is an ordering scheme which enables’ old’ information to be deleted when the memory is full. Hereditary and conjugacy properties are preserved to the maximum extent when minimizing a quadratic function subject to linear constraints. Practical experience is described on small (and some larger) CUTE test problems, and is reasonably encouraging, although there is some evidence of slow convergence on large problems with large null spaces.
    Original languageEnglish
    Title of host publicationSystem modeling and optimization
    Subtitle of host publicationproceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy
    EditorsF. Ceragioli, A. Dontchev, H. Furuta, K. Marti, L. Pandolfi
    Place of PublicationNew York
    PublisherSpringer
    Pages275-293
    ISBN (Print)9780387327747, 9781441941039
    DOIs
    Publication statusPublished - 2006

    Publication series

    NameIFIP Advances in Information and Communication Technology
    PublisherSpringer
    Number199
    ISSN (Print)1868-4238

    Fingerprint

    Quasi-Newton
    Nonlinear Programming
    Update
    Null Space
    Positive semidefinite
    Conjugacy
    Linear transformation
    Linear Constraints
    Quadratic Function
    Quadratic Programming
    Test Problems
    Updating
    Invariance
    Approximation

    Keywords

    • Nonlinear programming
    • Filter
    • SQP
    • Quasi-Newton
    • Symmetric rank one
    • Limited memory

    Cite this

    Fletcher, R. (2006). A new low-rank quasi-Newton update scheme for nonlinear programming. In F. Ceragioli, A. Dontchev, H. Furuta, K. Marti, & L. Pandolfi (Eds.), System modeling and optimization: proceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy (pp. 275-293). (IFIP Advances in Information and Communication Technology; No. 199). New York: Springer . https://doi.org/10.1007/0-387-33006-2_25
    Fletcher, R. / A new low-rank quasi-Newton update scheme for nonlinear programming. System modeling and optimization: proceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy. editor / F. Ceragioli ; A. Dontchev ; H. Furuta ; K. Marti ; L. Pandolfi. New York : Springer , 2006. pp. 275-293 (IFIP Advances in Information and Communication Technology; 199).
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    Fletcher, R 2006, A new low-rank quasi-Newton update scheme for nonlinear programming. in F Ceragioli, A Dontchev, H Furuta, K Marti & L Pandolfi (eds), System modeling and optimization: proceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy. IFIP Advances in Information and Communication Technology, no. 199, Springer , New York, pp. 275-293. https://doi.org/10.1007/0-387-33006-2_25

    A new low-rank quasi-Newton update scheme for nonlinear programming. / Fletcher, R.

    System modeling and optimization: proceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy. ed. / F. Ceragioli; A. Dontchev; H. Furuta; K. Marti; L. Pandolfi. New York : Springer , 2006. p. 275-293 (IFIP Advances in Information and Communication Technology; No. 199).

    Research output: Chapter in Book/Report/Conference proceedingChapter

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    AB - A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden family, although invariance under linear transformations of the variables is preserved. The representation provides a limited memory capability, and there is an ordering scheme which enables’ old’ information to be deleted when the memory is full. Hereditary and conjugacy properties are preserved to the maximum extent when minimizing a quadratic function subject to linear constraints. Practical experience is described on small (and some larger) CUTE test problems, and is reasonably encouraging, although there is some evidence of slow convergence on large problems with large null spaces.

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    KW - Filter

    KW - SQP

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    Fletcher R. A new low-rank quasi-Newton update scheme for nonlinear programming. In Ceragioli F, Dontchev A, Furuta H, Marti K, Pandolfi L, editors, System modeling and optimization: proceedings of the 22nd IFIP TC7 Conference held from , July 18-22, 2005, Turin, Italy. New York: Springer . 2006. p. 275-293. (IFIP Advances in Information and Communication Technology; 199). https://doi.org/10.1007/0-387-33006-2_25