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Preliminaries

  1. Convex sets
    • 1.1 Convex combination
    • 1.2 Convex sets
    • 1.3 Examples of convex sets
    • 1.4 Properties of convex sets
  2. Functions of several variables
    • 2.1 Functions of several variables
    • 2.2 Gradient, Hessian and level sets
    • 2.3 Examples of functions that are not quadratic
  3. Convex and concave functions
    • 3.1 Convex functions
    • 3.2 Concave functions
    • 3.3 Examples of convex and concave functions
    • 3.4 Convex functions defined by norms
    • 3.5 Properties of convex and concave functions
  4. Quadratic functions
    • 4.1 Quadratic functions
    • 4.2 Gradient, Hessian and level sets
    • 4.3 Convexity of quadratic functions
    • 4.4 Quadratic functions with a linear part

Optimization problems

  1. Optimization problems
    • 5.1 Optimization problems
    • 5.2 Properties of optimization problems
    • 5.3 Local and global optimal solutions
  2. Convex and concave optimization problems
    • 6.1 Convex and concave optimization problems
    • 6.2 Local optima of convex and concave problems
    • 6.3 Examples of convex and concave optimization problems