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
a natural stationarity measure, thus establishing the first result of this kind for a diminishing
stepsize method for nonconvex, constrained optimization problems.