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. We then consider the particular case in which the constraints are convex and satisfy a standard constraint qualification and show that in this setting the algorithm can be considerably simplified, reducing the computational burden of each iteration.

Diminishing stepsize methods for nonconvex composite problems via ghost penalties: from the general to the convex regular constrained case / Facchinei, F.; Kungurtsev, V.; Lampariello, L.; Scutari, G.. - In: OPTIMIZATION METHODS & SOFTWARE. - ISSN 1055-6788. - 37:4(2022), pp. 1242-1268. [10.1080/10556788.2020.1854253]

Diminishing stepsize methods for nonconvex composite problems via ghost penalties: from the general to the convex regular constrained case

Facchinei F.
;
2022

Abstract

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. We then consider the particular case in which the constraints are convex and satisfy a standard constraint qualification and show that in this setting the algorithm can be considerably simplified, reducing the computational burden of each iteration.
2022
composite optimization; constrained optimization; diminishing stepsize; nonconvex optimization
01 Pubblicazione su rivista::01a Articolo in rivista
Diminishing stepsize methods for nonconvex composite problems via ghost penalties: from the general to the convex regular constrained case / Facchinei, F.; Kungurtsev, V.; Lampariello, L.; Scutari, G.. - In: OPTIMIZATION METHODS & SOFTWARE. - ISSN 1055-6788. - 37:4(2022), pp. 1242-1268. [10.1080/10556788.2020.1854253]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1474322
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