Optimisation and Approximation

The goal of this course is to present optimization techniques with a main focus on linear relaxation. Applications to approximation algorithms will be highlighted.

Contents of the course.

  1. Linear Programming.
    • Polytopes.
    • Simplex algorithm.
    • Duality and complementary slackness.
    • Sensitivity analysis.
    • Integer polytopes (flows, transportation, totally unimodular matrices).
    • Integrality gap, Erdos-Posa property.
    • VC-dimension.
  2. Approximation via linear relaxation.
    • Primal-Dual algorithms.
    • Branch and bound.
  3. Non linear optimization.
    • Semidefinite programming.
    • Convex optimization.


  • Understanding and Using Linear Programming, Matousek and Gartner (2006).
  • Linear Programming, Chvatal (1983).

  • Applied Mathematical Programming, Bradley, Hax, and Magnanti (1977).
  • The Design of Approximation Algorithms David P. Williamson and David B. Shmoys (2010).

Prerequisites for the course.
Students should know the basics from Calculus and Linear Algebra.

The webpage of the course.