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Incremental methods and String-Averaging for non-differentiable convex optimization with inaccurate Subgradients

Grant number: 15/10171-2
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): July 01, 2015
Effective date (End): June 30, 2017
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Elias Salomão Helou Neto
Grantee:Rafael Massambone de Oliveira
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID


"String averaging" algorithms for the convex feasibility problem, recently shown interesting properties in applications to computerized tomography when generalized appropriately. Until now the theory covers the differentiable convex case restricted to non-negative octant, but non-differentiable functions and more general constraints are of practical interest. This project aims to approach, the theoretical and practical points of view, the convergence of incremental algorithms and "string averaging" under more general conditions, even under the assumption of random error in the computation of subgradients. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
OLIVEIRA, R. M.; HELOU, E. S.; COSTA, E. F. String-averaging incremental stochastic subgradient algorithms. OPTIMIZATION METHODS & SOFTWARE, v. 34, n. 3, p. 665-692, MAY 4 2019. Web of Science Citations: 0.
DE OLIVEIRA, RAFAEL MASSAMBONE; HELOU, ELIAS SALOMAO; COSTA, EDUARDO FONTOURA. String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images. INVERSE PROBLEMS, v. 32, n. 11 NOV 2016. Web of Science Citations: 3.
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
OLIVEIRA, Rafael Massambone de. String-averaging incremental subgradient methods for constrained convex optimization problems. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação São Carlos.

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