TY - JOUR
T1 - Rates of convergence of a one-dimensional search based on interpolating polynomials
AU - Tamir, A.
PY - 1979/2
Y1 - 1979/2
N2 - 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.
AB - 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.
KW - Mathematical programming
KW - convergence rates
KW - interpolating polynomials
KW - line search procedures
UR - http://www.scopus.com/inward/record.url?scp=34250269934&partnerID=8YFLogxK
U2 - 10.1007/BF00933226
DO - 10.1007/BF00933226
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AN - SCOPUS:34250269934
VL - 27
SP - 187
EP - 203
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
IS - 2
ER -