n the first part of this talk, we study a convex-constrained nonsmooth DC program in which the concave summand of the objective is an infimum of possibly infinitely many smooth concave functions. We propose some algorithms by using nonmonotone linear search and extrapolation techniques for possible acceleration for this problem, and analyze their global convergence, sequence convergence and also iteration complexity. We also propose randomized counterparts for them and discuss their convergence.