Diminishing stepsize methods for nonconvex composite problems via ghost penalties: from the general to the convex regular constrained case

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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.
Funding Information
  • Progetto di Ateneo Distributed optimization algorithms for Big Data
  • OP VVV (CZ.02.1.01/0.0/0.0/16_019/0000765)
  • MIUR (PRIN 2017)
  • NSF (1564044, CIF 1719205, CMMI 1832688)
  • DOE (DE-OE0000921)
  • ARO (W911NF1810238)

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