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.
Facchinei, F., Kungurtsev, V., Lampariello, L., & Scutari, G. (2020). CONVERGENCE RATE FOR DIMINISHING STEPSIZE METHODS IN NONCONVEX CONSTRAINED OPTIMIZATION VIA GHOST PENALTIES. ATTI DELLA ACCADEMIA PELORITANA DEI PERICOLANTI, CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI, 98 [10.1478/AAPP.98S2A8].
CONVERGENCE RATE FOR DIMINISHING STEPSIZE METHODS IN NONCONVEX CONSTRAINED OPTIMIZATION VIA GHOST PENALTIES
Lampariello, L;
2020
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
