  Focusing on minimization problems with structured objective function and
smooth constraints, we present a flexible technique that combines the
beneficial regularization effects of (exact) penalty and interior-point
methods. Working in the fully nonconvex setting, a pure barrier approach
requires careful steps when approaching the infeasible set, thus hindering
convergence. We show how a tight integration with a penalty scheme overcomes
such conservatism, does not require a strictly feasible starting point, and
thus accommodates equality constraints. The crucial advancement that allows us
to invoke generic (possibly accelerated) subsolvers is a marginalization step:
amounting to a conjugacy operation, this step effectively merges (exact)
penalty and barrier into a smooth, full domain functional object. When the
penalty exactness takes effect, the generated subproblems do not suffer the
ill-conditioning typical of penalty methods, nor do they exhibit the
nonsmoothness of exact penalty terms. We provide a theoretical characterization
of the algorithm and its asymptotic properties, deriving convergence results
for fully nonconvex problems. Illustrative examples and numerical simulations
demonstrate the wide range of problems our theory and algorithm are able to
cover.
