A powerful iterative descent method for finding a local minimum of a function of several
variables is described. A number of theorems are proved to show that it always converges and …

A simple variation of the well-known method of minimizing a function of several variables by
changing one parameter at a time is described. This variation is such that when the …

… of some of the convergence properties of our method is reported elsewhere (Powell, 1977). …
Our numerical results and the convergence theory in Powell (1977) show that a superlinear …

Most functions that occur in mathematics cannot be used directly in computer calculations.
Instead they are approximated by manageable functions such as polynomials and piecewise …

Many different procedures have been proposed for optimization calculations when first
derivatives are not available. Further, several researchers have contributed to the subject, …

… d9, (4.8) 17 MJD POWELL which may be verified by integration … Because we have shown
that if 19 MJD POWELL k > kQ then … POWELL . to be no less than a constant positive multiple of …

The conjugate gradient method is particularly useful for minimizing functions of very many
variables because it does not require the storage of any matrices. However the rate of …

The most widely used oxide for photocatalytic applications owing to its low cost and high
activity is TiO 2 . The discovery of the photolysis of water on the surface of TiO 2 in 1972 1 …

This paper presents a method for efficient Radial basis function (RBF) evaluation if
compactly supported radial basis functions (CSRBF) are used. Application of CSRBF leads …

BOBYQA is an iterative algorithm for finding a minimum of a function F (x), x∈ Rn, subject to
bounds a≤ x≤ b on the variables, F being specified by a “black box” that returns the value …