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Quasi-Newton Methods

In: Linear and Nonlinear Programming

Author

Listed:
  • David G. Luenberger

    (Stanford University)

  • Yinyu Ye

    (Stanford University)

Abstract

In this chapter we take another approach toward the development of methods lying somewhere intermediate to steepest descent and Newton’s method. Again working under the assumption that evaluation and use of the Hessian matrix is impractical or costly, the idea underlying quasi-Newton methods is to use an approximation to the inverse Hessian in place of the true inverse that is required in Newton’s method. The form of the approximation varies among different methods—ranging from the simplest where it remains fixed throughout the iterative process, to the more advanced where improved approximations are built up on the basis of information gathered during the descent process.

Suggested Citation

  • David G. Luenberger & Yinyu Ye, 2016. "Quasi-Newton Methods," International Series in Operations Research & Management Science, in: Linear and Nonlinear Programming, edition 4, chapter 0, pages 285-317, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-18842-3_10
    DOI: 10.1007/978-3-319-18842-3_10
    as

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