In 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.

In the second part we consider a class of DC constrained nonsmooth DC programs. We propose penalty and
augmented Lagrangian methods for solving them and show that they converge to a B-stationary
point under much weaker assumptions than those imposed in the literature.

This is joint work with Zhe Sun and Zirui Zhou.