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)