Solving the Perceptron Problem by deterministic optimization approach based on DC programming and DCA

The Perceptron Problem (PP) appeared for the first time in the Learning Machines and is very useful for zero-knowledge identification schemes in cryptology. The problem is NP-complete and no deterministic algorithm is known to date. In this paper we develop a deterministic method based on DC (Difference of Convex functions) programming and DCA (DC optimization Algorithms), an innovative approach in nonconvex programming framework. We first formulate the PP as a concave minimization programming problem. Then, we show how to apply DC programming and DCA for the resulting problem. Numerical results demonstrate that the proposed algorithm is promising: its is very fast and can efficiently solve the Perceptron Problem with large sizes.