MATHEMATICAL ENGINEERING TECHNICAL REPORTS Continuous Relaxation for Discrete DC Programming

Discrete DC programming with convex extensible functions is studied. A natural approach for this problem is a continuous relaxation that extends the problem to a continuous domain and applies the algorithm in continuous DC programming. By employing a special form of continuous relaxation, which is named “lin-vex extension,” the optimal solution of the continuous relaxation coincides with the original discrete problem. The proposed method is demonstrated for the degree-concentrated spanning tree problem, the unfair flow problem, and the correlated knapsack problem. ∗A preliminary version of this paper is included in the Proceedings of the 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2015, Metz, May 13–15) — Part I, Advances in Intelligent Systems and Computing, vol.359, Springer, 2015, pp. 181–190.