Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization

This paper presents new versions of proximal bundle methods for solving convex constrained nondifferentiable minimization problems. The method employ 𝓁1 or 𝓁Å• exact penalty functions with new penalty updates that limit unnecessary penalty growth. In contrast to other methods, some of them are insensitive to problem function scaling. Global convergence of the methods is established, as well as finite termination for polyhedral problems. Some encouraging numerical experience is reported. The ideas presented may also be used in variable metric methods for smooth nonlinear programming.