Diminishing stepsize methods for nonconvex composite problems via ghost penalties: from the general to the convex regular constrained case. (4th July 2022)

• Record Type: Journal Article
• Authors: Facchinei, Francisco; Kungurtsev, Vyacheskav; Lampariello, Lorenzo; Scutari, Gesualdo
• Is Part Of: Optimization methods and software. Volume 37:Number 4(2022)
• Page Start: 1242
• Page End: 1268
• Publication Date: 2022-07-04
• Subjects: Constrained optimization -- nonconvex optimization -- composite optimization -- diminishing stepsize; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1854253
• Languages: English
• ISSNs: 1055-6788

Abstract

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.