Optimization using the gradient and simplex methods.

Traditionally optimization of analytical methods has been conducted using a univariate method, varying each parameter one-by-one holding fixed the remaining. This means in many cases to reach only local minima and not get the real optimum. Among the various options for multivariate optimization, this paper highlights the gradient method, which involves the ability to perform the partial derivatives of a mathematical model, as well as the simplex method that does not require that condition. The advantages and disadvantages of those two multivariate optimization methods are discussed, indicating when they can be applied and the different forms that have been introduced. Different cases are described on the applications of these methods in analytical chemistry.