Lecture Notes

  1. Introduction (ps, pdf, 2up)
  2. Convexity and Duality (ps, pdf, 2up)
  3. SDP Relaxations for Quadratic Programming (ps, pdf, 2up)
  4. Algebra and Duality (ps, pdf, 2up)
  5. The Algebraic Geometric Dictionary (ps, pdf, 2up)
  6. The Nullstellensatz (ps, pdf, 2up)
  7. Groebner Bases (ps, pdf, 2up)
  8. More Groebner Bases (ps, pdf, 2up)
  9. Elimination (ps, pdf, 2up)
  10. Sum of Squares (ps, pdf, 2up)
  11. Lifting (ps, pdf, 2up)
  12. The Positivstellensatz (ps, pdf, 2up)
  13. Semialgebraic Lifting (ps, pdf, 2up)
  14. Sparse Polynomials (ps, pdf, 2up)
  15. Fourier-Motzkin Elimination (ps, pdf, 2up)
  16. More Fourier-Motzkin Elimination (ps, pdf, 2up)