Rates of convergence of a one-dimensional search based on interpolating polynomials

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Abstract

In this study, we derive the order of convergence of line search techniques based on fitting polynomials, using function values as well as information on the smoothness of the function. Specifically, it is shown that, if the interpolating polynomial is based on the values of the function and its first s-1 derivatives at n+1 approximating points, the rate of convergence is equal to the unique positive root rn+1 of the polynomial {Mathematical expression} For all n, rn is bounded between s and s+1, which in turn implies that the rate can be increased by as much as one wishes, provided sufficient information on the smoothness is incorporated.

Original languageEnglish
Pages (from-to)187-203
Number of pages17
JournalJournal of Optimization Theory and Applications
Volume27
Issue number2
DOIs
StatePublished - Feb 1979

Keywords

  • Mathematical programming
  • convergence rates
  • interpolating polynomials
  • line search procedures

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