Optimization Methods Involving a Generalized Form of f y

Optimization Methods Involving a Generalized Form of f(y). If some generalized two or three parameter function can be postulated for fiy) then general optimization methods can be applied to determine the values of the parameters which produce the best agreement, when incorporated in equation (26), with the dataset, g, e.g. a criterion for convergence of the best-fit could be the root-mean-square (r.m.s.) relative deviation  

This method was successful in the first attempts to solve equation (15) using a local isotherm equation that allowed adsorbate lateral interactions within patches. The ingenious graphical method, now referred to as the Ross and Olivier method of analysis, has been described in their monograph and in a condensed account by Ross. The technique used by Ross and Olivier employs a Gaussian probability function for the distribution of adsorption energies, i.e. a two-parameter generalized distribution of the form  

The Solid-Gas Interface , ed. E. A. Flood, Marcel Dekker Inc., New York, 1967, Ch. 15. 

Kindle et al. also adopted this method but used another generalized distribution function, a Maxwell-Boltzmann (MB) distribution  

Although it is in principle feasible to fit a variety of generalized distribution functions to adsorption data using least-squares methods e.g. Powell algorithm or Simplex method, in practice multiple minima may arise hence considerable care is required in checking the domain of the parameters to obtain initial estimates and the uniqueness of the final solution. 

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