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.
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: http://hdl.handle.net/11590/379362
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