MIP Lifting Techniques for Mixed Integer Nonlinear Programs Jean-Philippe P. Richard* School of Industrial Engineering, Purdue University Mohit Tawarmalani.

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Presentation transcript:

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

MIP 2006, Thursday June 8th Structure of the Talk

MIP 2006, Thursday June 8th

4 A Motivation in Integer Programming

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

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

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

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

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

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

MIP 2006, Thursday June 8th

MIP 2006, Thursday June 8th Goal of Part II

MIP 2006, Thursday June 8th

MIP 2006, Thursday June 8th Mixed Integer Nonlinear Knapsack

MIP 2006, Thursday June 8th Mixed Integer Nonlinear Knapsack

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

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

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

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

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

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

MIP 2006, Thursday June 8th

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

MIP 2006, Thursday June 8th BMIKP: Comments

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

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

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

MIP 2006, Thursday June 8th Example

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

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

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

MIP 2006, Thursday June 8th Example

MIP 2006, Thursday June 8th

MIP 2006, Thursday June 8th

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

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

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

MIP 2006, Thursday June 8th High Rank Certificate

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

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

MIP 2006, Thursday June 8th

MIP 2006, Thursday June 8th Goal of Part III

MIP 2006, Thursday June 8th A General Procedure

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

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

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

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

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

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

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

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

MIP 2006, Thursday June 8th Obtaining the Convex Hull of Disjunctive Sets: A Result

MIP 2006, Thursday June 8th Obtaining the Convex Hull of Disjunctive Sets: An Example

MIP 2006, Thursday June 8th Obtaining the Convex Hull of Disjunctive Sets: An Example

MIP 2006, Thursday June 8th Some Comments

MIP 2006, Thursday June 8th

MIP 2006, Thursday June 8th Goal of Part IV

MIP 2006, Thursday June 8th Generalizing the Theory…

MIP 2006, Thursday June 8th Generalizing the Superadditive Lifting Theory…

MIP 2006, Thursday June 8th Application: Sequence Independent lifting for single-constraint problems

MIP 2006, Thursday June 8th Application: Sequence Independent lifting for single-constraint problems

MIP 2006, Thursday June 8th

MIP 2006, Thursday June 8th Conclusion & Future Work