LINE SEARCH TECHNIQUES BASED ON INTERPOLATING POLYNOMIALS USING FUNCTION VALUES ONLY.

In this study we derive the order of convergence of some line search techniques based on fitting polynomials, using function values only. It is shown that the order of convergence increases with the degree of the polynomial. If viewed as a sequence, the orders approach the Golden Section Ratio when the degree of the polynomial tends to infinity. [ABSTRACT FROM AUTHOR]