Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces

• Published in: Computational optimization and applications Vol. 78; no. 3; pp. 705 - 740
• Main Authors: Geiersbach, Caroline, Scarinci, Teresa
• Format: Journal Article
• Language: English
• Published: New York, NY Springer US 01.04.2021; Springer Nature B.V
• Subjects: Algorithms; Approximation; Constraints; Continuity (mathematics); Convergence; Convex and Discrete Geometry; Differential inclusions; Hilbert space; Management Science; Mathematical programming methods; Mathematics; Mathematics and Statistics; Nonsmooth and nonconvex optimization; Operations Research; Operations Research/Decision Theory; Optimal control problems involving partial differential equations; Optimization; Partial differential equations; Partial differential equations with randomness; Statistics; Stochastic programming; Differential inclusions; Optimal control problems involving partial differential equations; Partial differential equations with randomness; Nonsmooth and nonconvex optimization; Mathematical programming methods; Stochastic programming

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives. This paper presents convergence results for the stochastic pr...