1 / 63

MIP Lifting Techniques for Mixed Integer Nonlinear Programs

MIP Lifting Techniques for Mixed Integer Nonlinear Programs. Jean-Philippe P. Richard* School of Industrial Engineering, Purdue University Mohit Tawarmalani Krannert School of Management, Purdue University. *Supported by NSF DMI0348611. Structure of the Talk.

kipp
Download Presentation

MIP Lifting Techniques for Mixed Integer Nonlinear Programs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MIP Lifting Techniques for Mixed Integer Nonlinear Programs Jean-Philippe P. Richard* School of Industrial Engineering, Purdue University Mohit Tawarmalani Krannert School of Management, Purdue University *Supported by NSF DMI0348611

  2. Structure of the Talk MIP 2006, Thursday June 8th 2006

  3. MIP 2006, Thursday June 8th 2006

  4. A Motivation in Integer Programming MIP 2006, Thursday June 8th 2006

  5. A Motivation in Integer Programming MIP 2006, Thursday June 8th 2006

  6. What is MIP Lifting? MIP 2006, Thursday June 8th 2006

  7. Some Literature on MIP lifting MIP 2006, Thursday June 8th 2006

  8. What is Hard about MINLP Lifting? MIP 2006, Thursday June 8th 2006

  9. Overview & Goal of Our Work MIP 2006, Thursday June 8th 2006

  10. Some Nice Features of MINLP Lifting MIP 2006, Thursday June 8th 2006

  11. MIP 2006, Thursday June 8th 2006

  12. Goal of Part II MIP 2006, Thursday June 8th 2006

  13. MIP 2006, Thursday June 8th 2006

  14. Mixed Integer Nonlinear Knapsack MIP 2006, Thursday June 8th 2006

  15. Mixed Integer Nonlinear Knapsack MIP 2006, Thursday June 8th 2006

  16. Generating Valid Inequalities for PS MIP 2006, Thursday June 8th 2006

  17. A General Lifting Result for PS MIP 2006, Thursday June 8th 2006

  18. Advantages and Limitations of the Lifting Scheme MIP 2006, Thursday June 8th 2006

  19. A Superadditive Lifting Result for PS MIP 2006, Thursday June 8th 2006

  20. A Superadditive Lifting Result for PS MIP 2006, Thursday June 8th 2006

  21. A Superadditive Lifting Result for PS MIP 2006, Thursday June 8th 2006

  22. MIP 2006, Thursday June 8th 2006

  23. Application: Bilinear Mixed Integer Knapsack Problem (BMIKP) MIP 2006, Thursday June 8th 2006

  24. BMIKP: Comments MIP 2006, Thursday June 8th 2006

  25. The Convex Hull of PT’ is a Polyhedron MIP 2006, Thursday June 8th 2006

  26. Obtaining Facets of PT using Superadditive Lifting MIP 2006, Thursday June 8th 2006

  27. Obtaining Facets of PT using Superadditive Lifting MIP 2006, Thursday June 8th 2006

  28. Example MIP 2006, Thursday June 8th 2006

  29. Obtaining Facets of PT using Superadditive Lifting MIP 2006, Thursday June 8th 2006

  30. Another Family of Strong Inequalities for PT MIP 2006, Thursday June 8th 2006

  31. Another Family of Strong Inequalities for PT MIP 2006, Thursday June 8th 2006

  32. Example MIP 2006, Thursday June 8th 2006

  33. MIP 2006, Thursday June 8th 2006

  34. MIP 2006, Thursday June 8th 2006

  35. An Equivalent Integer Programming Formulation for PT MIP 2006, Thursday June 8th 2006

  36. An Equivalent Integer Programming Formulation for PT MIP 2006, Thursday June 8th 2006

  37. Strong Rank-1 Inequalities MIP 2006, Thursday June 8th 2006

  38. High Rank Certificate MIP 2006, Thursday June 8th 2006

  39. Lifted Cover Cuts for BMIKP are not Strong Rank-1 MIP 2006, Thursday June 8th 2006

  40. Towards the Next Step… MIP 2006, Thursday June 8th 2006

  41. MIP 2006, Thursday June 8th 2006

  42. Goal of Part III MIP 2006, Thursday June 8th 2006

  43. A General Procedure MIP 2006, Thursday June 8th 2006

  44. Deriving Nonlinear Cuts for Mixed Integer Programs: Applications MIP 2006, Thursday June 8th 2006

  45. Obtaining the Convex Hull of a Simple Bilinear Knapsack Set MIP 2006, Thursday June 8th 2006

  46. Obtaining the Convex hull of a Simple Bilinear Knapsack Set MIP 2006, Thursday June 8th 2006

  47. Obtaining the Convex hull of a Simple Bilinear Knapsack Set MIP 2006, Thursday June 8th 2006

  48. Obtaining the Convex hull of a Simple Bilinear Knapsack Set MIP 2006, Thursday June 8th 2006

  49. Obtaining Convex Hulls of Disjunctive Sets: An Example MIP 2006, Thursday June 8th 2006

  50. Obtaining Convex Hulls of Disjunctive Sets: An Example MIP 2006, Thursday June 8th 2006

More Related