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;
2020-01-01

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.
2020
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/379362
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