Optimisation modified simplex method

G. A. Zachariadis and J. A. Stratis, Optimisation of cold vapour atomic absorption spectrometric determination of mercury with and without amalgamation by subsequent use of complete and fractional factorial designs with univariate and modified simplex methods, J. Anal. At. Speetrom., 6(3), 1991, 239-245. 

A. P. Wade, Optimisation of Flow Injection Analysis and Polarography by the Modified Simplex Method. Anal. Proc., 20 (1983) 523. 

G. H. Lee, Development of new high temperature plasma sources for spectrochemical analysis multivariate optimisation by the modified sequential simplex method. Bull. Korean Chem. Soc., 14(2), 1993, 275-281. 

A weakness with the standard mediod for simplex optimisation is a dependence on the initial step size, which is defined by the initial conditions. For example, in Figure 2.37 we set a very small step size for both variables this may be fine if we are sure we are near the optimum, but otherwise a bigger triangle would reach the optimum quicker, the problem being that the bigger step size may miss the optimum altogether. Another method is called the modified simplex algorithm and allows the step size to be altered, reduced as the optimum is reached, or increased when far from the optimum. 

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