# Basics of parameter estimation / optimization

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## Polytope

### Introduction

The polytop method is one of the derivation-free optimization methods. The process is often called Simplex II in the literature.

The polytop method is often used in the optimization of tasks with numerous parameters. The method only works with objective function values, derivatives are not used (derivative-free method). Furthermore, the method allows the simple introduction of secondary conditions.

In the case of an n-dimensional problem, i.e. n optimal parameter values ​​are sought, a simplex is set up. A simplex is a polyhedron of dimension n with n + 1 vertices. It has the property that all associated points form a convex set. Thus, every point on the line connecting two simplex points belongs to the simplex itself. For n = 2 there is a triangle and for n = 3 a tetrahedron etc.

Convex set: A convex set is a set in which, if you connect any two points of the set, all points that lie on the connecting line also belong to the set.

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