Algorithm Nelder Mead sequential simplex

A polynomial was fit to the calibration curve for the thermocouple by means of a minimization of the maximum deviation technique using the Nelder Mead sequential simplex minimization algorithm method.( 5,6, 7) The coefficients of this polynomial are stored in the analysis program and are used to convert thermocouple voltages to temperature values. Y values are converted to dH(t,T)/dt, the heat flow into and out of the sample in mcal/sec. The operator selects a baseline for the analysis by entering the temperatures of the beginning and end points of the baseline. A plot is produced of the raw data with the operator selected baseline shown as illustrated in Figure A. 

There are two basic types of unconstrained optimization algorithms (I) those reqmring function derivatives and (2) those that do not. The nonderivative methods are of interest in optimization applications because these methods can be readily adapted to the case in which experiments are carried out directly on the process. In such cases, an ac tual process measurement (such as yield) can be the objec tive function, and no mathematical model for the process is required. Methods that do not reqmre derivatives are called direc t methods and include sequential simplex (Nelder-Meade) and Powell s method. The sequential simplex method is quite satisfac tory for optimization with two or three independent variables, is simple to understand, and is fairly easy to execute. Powell s method is more efficient than the simplex method and is based on the concept of conjugate search directions. 

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