Preliminaries

Part 1 of the course, volume 1 of the lecture notes. Convex combinations and convex sets, functions of several variables (gradient, Hessian, level sets), norms, convex and concave functions, quadratic functions and their convexity.

Lecture notes, volume 1 (PDF)

• 1. Convex sets

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  Convex combination · Convex sets · Examples of convex sets · Properties of convex sets

  Read the chapter · Exercises

• 2. Functions of several variables

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  Functions of several variables · Gradient, Hessian and level sets · Examples of functions that are not quadratic

  Read the chapter · Exercises

• 3. Convex and concave functions

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  Convex functions · Concave functions · Examples of convex and concave functions · Convex functions defined by norms · …

  Read the chapter · Exercises

• 4. Quadratic functions

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  Quadratic functions · Gradient, Hessian and level sets · Convexity of quadratic functions · Quadratic functions with a linear part

  Read the chapter · Exercises