1. Robust Optimization and Applications in Machine Learning
Laurent El Ghaoui
SAC Capital and UC Berkeley
IMS Tutorial, N.U. Singapore,
January 9, 2006

2. Thanks

3. Outline

4. Part 1: Overview of robust optimization

5. Optimization models

6. Pitfalls

7. Robust Optimization Paradigm

8. Approximating a robust solution

9. LP as a conic problem

10. Second-order cone programming

11. Semidefinite programming

12. Dual form of conic program

13. Robust conic programming

14. Polytopic uncertainty

15. Robust LP

16. Robust LP with ellipsoidal uncertainty

17. Robust LP as SOCP

18. Example: robust portfolio design

19. Solution of robust portfolio problem

20. Robust SOCP

21. Example: robust least-squares

22. Robust SDP

23. Example: robust control

24. Analysis of robust conic problems

25. Relaxations

26. Quality estimates

27. Quality estimates: some results

28. Restriction

29. Sampling

30. Robust Optimization: challenges

31. Robust optimization in machine learning

32. Part 1: summary