A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact version of the DC algorithm, where each subproblem is solved only approximately by a bundle method. We always terminate the bundle method after the...

Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions arising in practical applications such as low rank matrix factorization or deep neural network problems do not have a...

Gradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function and derivative information may be corrupted by noise,...

A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact version of the DC algorithm, where each subproblem is solved only approximately by a bundle method. We always terminate the bundle method after the...