Rosenbrock minimization

Edgar and Himmelblau (1988) demonstrate the use of the method for a function of two variables. Nelder and Mead (1965) presented the method for a function of N variables as a flow diagram. They demonstrated its use by applying it to minimize Rosenbrock s function (Equation 5.22) as well as to the following functions ... 

Will Newton s method minimize Rosenbrock s function... 

Example 2.4.1 Minimization of the Rosenbrock function by the simplex method of Nelder and Mead... 

Rosenbrock s function is often used as a minimization test problem, because its minimum lies at the base of a banana-shaped valley and can be difficult to locate. This function is defined for even integers n as the sum... 

Identification of the theoretical and experimental transfer functions in order to estimate the effective diffusivity De is obtained by minimizing a relative error function taken between the two transfer functions. The Rosenbrock method of optimization has been used. All the measurements have been made at room temperature and something close to normal atmospheric pressure. The only parameter that changes is the carrier gas flow rate. 

The set of integrated data, Ij, I2 and I3 were determined for each of the 75 data sets. The activity parameters and their temperature and pressure dependencies were found using Rosenbrock s parameter search technique (4 ) which minimized the sums of squares deviation as calculated from equation 9. The temperature and pressure dependence of the activity parameters were determined relative to base conditions of 900°F (756 K) and 177 psia H2. parameters are expressed in terms of process conditions as... 

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