MIP Lifting Techniques for Mixed Integer Nonlinear Programs
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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 DMI
2 Structure of the Talk MIP, Thursday June 8th 2
3 MIP, Thursday June 8th 3
4 A Motivation in Integer Programming MIP, Thursday June 8th 4
5 A Motivation in Integer Programming MIP, Thursday June 8th 5
6 What is MIP Lifting? MIP, Thursday June 8th 6
7 Some Literature on MIP lifting MIP, Thursday June 8th 7
8 What is Hard about MINLP Lifting? MIP, Thursday June 8th 8
9 Overview & Goal of Our Work MIP, Thursday June 8th 9
10 Some Nice Features of MINLP Lifting MIP, Thursday June 8th 10
11 MIP, Thursday June 8th 11
12 Goal of Part II MIP, Thursday June 8th 12
13 MIP, Thursday June 8th 13
14 Mixed Integer Nonlinear Knapsack MIP, Thursday June 8th 14
15 Mixed Integer Nonlinear Knapsack MIP, Thursday June 8th 15
16 Generating Valid Inequalities for PS MIP, Thursday June 8th 16
17 A General Lifting Result for PS MIP, Thursday June 8th 17
18 Advantages and Limitations of the Lifting Scheme MIP, Thursday June 8th 18
19 A Superadditive Lifting Result for PS MIP, Thursday June 8th 19
20 A Superadditive Lifting Result for PS MIP, Thursday June 8th 20
21 A Superadditive Lifting Result for PS MIP, Thursday June 8th 21
22 MIP, Thursday June 8th 22
23 Application: Bilinear Mixed Integer Knapsack Problem (BMIKP) MIP, Thursday June 8th 23
24 BMIKP: Comments MIP, Thursday June 8th 24
25 The Convex Hull of PT is a Polyhedron MIP, Thursday June 8th 25
26 Obtaining Facets of PT using Superadditive Lifting MIP, Thursday June 8th 26
27 Obtaining Facets of PT using Superadditive Lifting MIP, Thursday June 8th 27
28 Example MIP, Thursday June 8th 28
29 Obtaining Facets of PT using Superadditive Lifting MIP, Thursday June 8th 29
30 Another Family of Strong Inequalities for PT MIP, Thursday June 8th 30
31 Another Family of Strong Inequalities for PT MIP, Thursday June 8th 31
32 Example MIP, Thursday June 8th 32
33 MIP, Thursday June 8th 33
34 MIP, Thursday June 8th 34
35 An Equivalent Integer Programming Formulation for PT MIP, Thursday June 8th 35
36 An Equivalent Integer Programming Formulation for PT MIP, Thursday June 8th 36
37 Strong Rank-1 Inequalities MIP, Thursday June 8th 37
38 High Rank Certificate MIP, Thursday June 8th 38
39 Lifted Cover Cuts for BMIKP are not Strong Rank-1 MIP, Thursday June 8th 39
40 Towards the Next Step MIP, Thursday June 8th 40
41 MIP, Thursday June 8th 41
42 Goal of Part III MIP, Thursday June 8th 42
43 A General Procedure MIP, Thursday June 8th 43
44 Deriving Nonlinear Cuts for Mixed Integer Programs: Applications MIP, Thursday June 8th 44
45 Obtaining the Convex Hull of a Simple Bilinear Knapsack Set MIP, Thursday June 8th 45
46 Obtaining the Convex hull of a Simple Bilinear Knapsack Set MIP, Thursday June 8th 46
47 Obtaining the Convex hull of a Simple Bilinear Knapsack Set MIP, Thursday June 8th 47
48 Obtaining the Convex hull of a Simple Bilinear Knapsack Set MIP, Thursday June 8th 48
49 Obtaining Convex Hulls of Disjunctive Sets: An Example MIP, Thursday June 8th 49
50 Obtaining Convex Hulls of Disjunctive Sets: An Example MIP, Thursday June 8th 50
51 Obtaining Convex Hulls of Disjunctive Sets: An Example MIP, Thursday June 8th 51
52 Obtaining the Convex Hull of Disjunctive Sets: A Result MIP, Thursday June 8th 52
53 Obtaining the Convex Hull of Disjunctive Sets: An Example MIP, Thursday June 8th 53
54 Obtaining the Convex Hull of Disjunctive Sets: An Example MIP, Thursday June 8th 54
55 Some Comments MIP, Thursday June 8th 55
56 MIP, Thursday June 8th 56
57 Goal of Part IV MIP, Thursday June 8th 57
58 Generalizing the Theory MIP, Thursday June 8th 58
59 Generalizing the Superadditive Lifting Theory MIP, Thursday June 8th 59
60 Application: Sequence Independent lifting for single-constraint problems MIP, Thursday June 8th 60
61 Application: Sequence Independent lifting for single-constraint problems MIP, Thursday June 8th 61
62 MIP, Thursday June 8th 62
63 Conclusion & Future Work MIP, Thursday June 8th 63
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