privacy preserving linear programming l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Privacy-Preserving Linear Programming PowerPoint Presentation
Download Presentation
Privacy-Preserving Linear Programming

Loading in 2 Seconds...

play fullscreen
1 / 26

Privacy-Preserving Linear Programming - PowerPoint PPT Presentation


  • 112 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Privacy-Preserving Linear Programming' - brooklyn


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
privacy preserving linear programming

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
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
linear programming constraint matrix

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
Outline
  • Vertically (horizontally) partitioned linear program
  • Secure transformation via a random matrix
  • Privacy-preserving linear program solution
  • Computational results
  • Summary
vertically partitioned data each entity holds different variables for the same constraints

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
LP with Vertically Partitioned Data

We consider the linear program:

slide16

A1

A2

A3

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

A3

A1

A2

lp with horizontally partitioned data
LP with Horizontally Partitioned Data

We consider the linear program:

summary outlook
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
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