Chapter 01: Mathematical Concepts
This chapter introduces the basic mathematical concepts that are prerequisite for most optimization methods.

Chapter 1.1: Differentiability
In this section, we refresh the basic concept of differentiability for univariate and multivariate functions and introduce concepts such as the Jacobi or Hessian Matrix.

Chapter 1.2: Taylor Approximation
In this section, we explain both the univariate and the multivariate Taylor polynomial. Download »slidesconcepts2taylor.pdf«

Chapter 1.3: Convexity
In this section, we introduce the concept of convexity and briefly touch upon its importance for optimization.

Chapter 1.4: Conditions for optimality
In this section, we discuss several aspects of optima. Download »slidesconcepts4conditionsforoptimality.pdf«

Chapter 1.5: Quadratic forms I
In part one of this twopart section, we combine previously covered concepts to introduce both univariate and multivariate quadratic forms. Download »slidesconcepts5quadraticformsI.pdf«

Chapter 1.6: Quadratic forms II
In part two of this twopart section, we dive deeper into the properties of quadratic functions and their interpretation. Download »slidesconcepts6quadraticformsII.pdf«

Chapter 1.7: Matrix calculus
In this section, we connect the gradient, Jacobian and Hessian matrix with the concept of Matrix calculus.