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In this paper we first extend the diminishing stepsize method for nonconvexconstrained problems presented in [4] to deal with equality constraints and anonsmooth objective function of composite type. We then consider the particularcase in which the constraints are convex and satisfy a standard constraintqualification and show that in this setting the algorithm can be considerablysimplified, reducing the computational burden of each iteration.

Diminishing Stepsize Methods for Nonconvex Composite Problems via Ghost Penalties: from the General to the Convex Regular Constrained Case