##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Olvi Mangasarian

#### UCSD and University of Wisconsin, Madison

## Privacy-Preserving Linear Programming

##### Abstract:

By utilizing machine learning techniques for privacy-preserving classification, we consider linear programs with partitioned constraint matrices with each partition belonging to an entity that is unwilling to share its partition or make it public. For vertically partitioned matrices we employ a random matrix transformation that generates a linear program based on all the privately held data but without revealing the data or making it public. The component groups of the solution of the transformed problem can be decoded and made public only by the original group that owns the corresponding constraint matrix columns. For a horizontally partitioned constraint matrix, we multiply each partition by an appropriately generated and privately held constraint matrix. This results in an equivalent linear program that does not reveal any of the original data or make it public. The solution vector of the transformed linear program is publicly generated and is available to all entities.

### January 11, 2011

### 10:00 AM

### AP&M 2402

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