A New Algorithm for Privacy-Preserving Horizontally Partitioned Linear Programs

In a linear programming for horizontally partitioned data, the equality constraint matrix is divided into groups of rows. Each group of the matrix rows and the corresponding right-hand side vector are owned by different entities, and these entities are reluctant to disclose their own groups of rows or right-hand side vectors. To calculate the optimal solution for the linear programming in this case, Mangasarian used a random matrix of full rank with probability 1, but an event with probability 1 is not a certain event, so a random matrix of full rank with probability 1 does not certainly happen. In this way, the solution of the original linear programming is not equal to the solution of the secure linear programming. We used an invertible random matrix for this shortcoming. The invertible random matrix converted the original linear programming problem to a secure linear program problem. This secure linear programming will not reveal any of the privately held data.