Penalty and Augmented Lagrangian Methods for Constrained DC Programming

In this paper, we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC programs in which the first convex component objective and constraints is sum smooth function, their second supremum finitely many functions. The existing methods for problem usually have weak convergence guarantee or require feasible initial point. Inspired by recent work Pang et al. [Pang J-S, Razaviyayn M, Alvarado A (2017) Computing B-stationary points programs. Math. Oper. Res. 42(1):95–118.], propose two infeasible with strong considered problem. one penalty method that consists finding an approximate D-stationary point sequence subproblems. We show any accumulation solution generated such under weakest possible assumption it satisfies pointwise Slater constraint qualification (PSCQ). augmented Lagrangian (AL) AL Under same PSCQ condition as method, problem, moreover, Karush–Kuhn–Tucker type optimality together set auxiliary multipliers. also efficient successive approximation computing Finally, some numerical experiments are conducted to demonstrate efficiency our proposed methods.