Privacy-Preserving Linear Programming

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# Privacy-Preserving Linear Programming - PowerPoint PPT Presentation

Privacy-Preserving Linear Programming. UCSD – Center for Computational Mathematics Seminar January 11, 2011. Olvi Mangasarian UW Madison & UCSD La Jolla. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A A A A. Problem Statement.

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## Privacy-Preserving Linear Programming

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### Privacy-Preserving Linear Programming

UCSD – Center for Computational Mathematics Seminar

January 11, 2011

Olvi Mangasarian

UW Madison & UCSD La Jolla

TexPoint fonts used in EMF.

Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAA

Problem Statement
• Entities with related data wish to solve a linear program based on all the data
• The entities are unwilling to reveal their data to each other
• If each entity holds a different set of variables for all constraints, then the data is said to be vertically partitioned
• If each entity holds a different set of constraints with all variables, then the data is said to be horizontally partitioned
• Our approach: privacy-preserving linear programming (PPLP) using random matrix transformations
• Provides exact solution to the total linear program
• Does not reveal any private information

Horizontally Partitioned Matrix

Vertically Partitioned Matrix

Linear Programming Constraint Matrix

Variables

1 2 ..………….…………. n

1

2

........m

A

A1

A¢1

A¢2

A¢3

Constraints

A2

A3

Outline
• Vertically (horizontally) partitioned linear program
• Secure transformation via a random matrix
• Privacy-preserving linear program solution
• Computational results
• Summary

A¢1

A¢2

A¢3

Vertically Partitioned Data:Each entity holds different variables for the same constraints

A¢1

A¢2

A¢3

LP with Vertically Partitioned Data

We consider the linear program:

A1

A2

A3

Horizontally Partitioned Constraint Matrix:Entities hold different constraints with the same variables

A3

A1

A2

LP with Horizontally Partitioned Data

We consider the linear program:

Summary & Outlook
• Based on a transformation using a random matrix B
• Get exact solution to the original linear program without revealing privately held data

Privacy preserving linear programming

for vertically or horizontally partitioned data

Possible extensions to: horizontally partitioned inequality constraints, complementarity problems and nonlinear programs

References

ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/10-01.pdf

ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/10-02.pdf

Optimization Letters, to appear