\[\newcommand{\u}[1]{\boldsymbol{\mathsf{#1}}} \renewcommand{\b}[1]{\boldsymbol{#1}} \newcommand{\t}[1]{\textsf{#1}} \newcommand{\m}[1]{\mathbb{#1}} \def\RR{\bf R} \def\bold#1{\bf #1} \def\mbf#1{\mathbf #1} \def\uv#1{\hat{\usf {#1}}} \def\dl#1{\underline{\underline{#1}}} \newcommand{\usf}[1]{\boldsymbol{\mathsf{#1}}} \def\bs#1{\usf #1}\]

• Notation
• Basic Definitions
• Finite Dimensions Necessary and Sufficient Conditions
  • Global minimizers
  • Local minimizers
• Derivatives and Taylor’s theorem
  • One dimension
  • Finite Dimensions

Note: It is more informative if a necessary condition is not satisfied and a sufficient condition is satisfied.

Note: Hessian is different from a Hessian-matrix.

Note: A if B, or If B then A, means that B is a sufficient condition. In this case, A can be true even with B not being true. \(B \Rightarrow A\).

Note: A only if B, or A then B, means that B is a necessary condition. In this case, A cannot be true without B also being true. However, B being true does not necessary mean that A is true. \(A \Rightarrow B\).

• Calculus of Variations
  • Maximize Entropy (Example with two constraints)

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