Diminishing stepsize methods for nonconvex composite problems via ghost penalties: from the general to the convex regular constrained case. (4th July 2022) - Facchinei, Francisco; Kungurtsev, Vyacheskav; Lampariello, Lorenzo; Scutari, Gesualdo
ABSTRACT: In this paper, we first extend the diminishing stepsize method for nonconvex constrained problems presented in F. Facchinei, V. Kungurtsev, L. Lampariello and G. Scutari [ Ghost penalties in nonconvex constrained optimization: Diminishing stepsizes and iteration complexity, To appear on Math. Oper. Res. 2020. Available at https://arxiv.org/abs/1709.03384 .] to deal with equality constraints and a nonsmooth objective function of composite type. We then consider the particular case in which the constraints are convex and satisfy a standard constraint qualification and show that in this setting the algorithm can be considerably simplified, reducing the computational burden of each iteration.