Abstract
Formulation of the simplex matrix referred to n-D space, is presented in terms of the scalar product of vectors, known from elementary algebra. The principles of a simplex optimization procedure are presented on a simple example, with use of a target function taken as a criterion of optimization, where accuracy and precision are treated equally in searching optimal conditions of a gravimetric analysis.
Highlights
Simplex is a geometric figure, formed on the basis of n +1 points Ai (i = 0, n) in the n-dimensional space, i.e., a number of the points exceeds the dimension of the space by one
Specifying the coordinates for Ai is easy if it concerns the 2-D or 3-D space, but it becomes less comprehensible when the issue concerns the n-dimensional (n-D) simplex
The simplex concept is the basis for the Nelder-Mead [2] simplex optimization procedure (SOP) [3], conceived as a modification of the simplex method of Spendley, Hext and Himsworth [4]
Summary
Simplex is a geometric figure, formed on the basis of n +1 points Ai (i = 0, , n) in the n-dimensional space, i.e., a number of the points exceeds the dimension of the space by one. Michałowski is widely applicable and popular in different fields of chemistry, chemical engineering, and medicine [9]. It works well in practice on a wide variety of problems, where real-valued minimization functions with scalar variables are applied. The problem of obtaining the simplex matrix in n-D space will be presented on the basis of the triangle and the scalar product concept, well-known to the students from earlier stages of education. The evolution of the simplex according to SOP [3] [18] will be presented in a understandable manner
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