Recent Advances in DC Programming and DCA

Difference of Convex functions (DC) Programming and DC Algorithm (DCA) constitute the backbone of Nonconvex Programming and Global Optimization. The paper is devoted to the State of the Art with recent advances of DC Programming and DCA to meet the growing need for nonconvex optimization and global optimization, both in terms of mathematical modeling as in terms of efficient scalable solution methods. After a brief summary of these theoretical and algorithmic tools, we outline the main results on convergence of DCA in DC programming with subanalytic data, exact penalty techniques with/without error bounds in DC programming including mixed integer DC programming, DCA for general DC programs, and DC programming involving the l(0)-norm via its approximation and penalization.