Projected Stochastic Gradients for Convex Constrained Problems in Hilbert Spaces

Geiersbach C & Pflug G ORCID: https://orcid.org/0000-0001-8215-3550 (2019). Projected Stochastic Gradients for Convex Constrained Problems in Hilbert Spaces. SIAM Journal on Optimization 29 (3): 2079-2099. DOI:10.1137/18M1200208.

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Abstract

Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates un converges weakly to a point in the set of minimizers with probability one. In the strongly convex case, the sequence converges strongly to the unique optimum with probability one. An application to a class of PDE constrained problems with a convex objective, convex constraint, and random elliptic PDE constraints is shown. Theoretical results are demonstrated numerically.

Item Type: Article
Research Programs: Risk & Resilience (RISK)
Depositing User: Luke Kirwan
Date Deposited: 28 Oct 2019 07:29
Last Modified: 28 Oct 2019 07:29
URI: http://pure.iiasa.ac.at/16129

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