# Generalized Bundle Methods

We propose a class of generalized Bundle methods where the stabilizi=
term can be any closed convex function satisfying certain properties. =
We prove finite termination, asymptotic convergence and finite convergenc=
e to an optimal point of different variants of the algorithm: for some of=
these proofs, f-regularity of the function (a new generalization of inf-=
compactness) is required. Our analysis gives a unified convergence proof =
for several classes of Bundle methods that have been so far regarded as d=
istinct, enhancing on the results known for some of them: furthermore, it=
covers methods proposed in the literature that had not previously been r=
ecognised as Bundle methods. A novelty in our approach is the proposal of=
a dual for the minimization problem: we show that Bundle methods can be =
seen as a dual ascent approach to one single nonlinear problem in the dua=
l space, where nonlinear subproblems are approximately solved at each ste=
p with an inner linearization approach. This interpretation is particular=
ly