title: Optimization using the gradient and simplex methods.
abstract: 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.
authors.affiliation: Chemistry Department, University of the Balearic Islands, 07122 Palma de Mallorca, Spain. Electronic address: victor.cerda@uib.es.
authors.forename: Víctor
authors.initials: V
authors.lastname: Cerdà
authors.affiliation: Department of Applied Mathematics and Analysis, University of Barcelona, Spain.
authors.forename: Juan Luis
authors.initials: JL
authors.lastname: Cerdà
authors.affiliation: Department of Chemistry, College of Science, King Khalid University, Abha 61321, Saudi Arabia.
authors.forename: Abubakr M
authors.initials: AM
authors.lastname: Idris
keywords: Gradient; Maximum slope; Multivariate optimization; Simplex