A Secure Revised Simplex Algorithm for Privacy-Preserving Linear Programming

Linear programming is one of the most widely applied solutions to optimization problems. This paper presents a privacy-preserving solution to linear programming for two parties when the cost, or objective, function is known only to one party, and the constraint equations are known only to the other party. An algorithm based on revised simplex is given that ensures that neither party gains access to the otherpsilas private information. While this has been proposed before, our solution is significantly more efficient for the given data distribution. This enables collaboration among companies in many domains, enhancing efficiency while maintaining competitiveness.