Ricerc@Sapienza

This is a companion paper to “Ghost penalties in nonconvex constrained
optimization: Diminishing stepsizes and iteration complexity" (to appear in Mathematics of
Operations Research). We consider the ghost penalty scheme for nonconvex, constrained
optimization introduced in that paper, coupled with a diminishing stepsize procedure. Under
an extended Mangasarian-Fromovitz-type constraint qualification we give an expression for
the maximum number of iterations needed to achieve a given solution accuracy according to

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.