The impact and the usefulness of difference convex optimization techniques for the numerical solution of problems arising in nonsmooth and nonconvex computational mechanics are investigated in this paper. Algorithms for the numerical solution of the problem are proposed and studied. The relation to the more general quasi- and co-differentiable optimization techniques is also discussed. The link to classical, smooth and nonsmooth computational mechanics' algorithms is also presented. Difference convex, quasi-differentiability, relaxation method, nonsmooth optimization, nonsmooth mechanics.