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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the differentiability check in gradient sampling methods

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Author(s):
Helou, Elias Salomao ; Santos, Sandra A. ; Simoes, Lucas E. A.
Total Authors: 3
Document type: Journal article
Source: OPTIMIZATION METHODS & SOFTWARE; v. 31, n. 5, p. 983-1007, OCT 2016.
Web of Science Citations: 3
Abstract

The present study aims to carefully discuss the importance of differentiability checks during the execution of methods based on gradient sampling. We stress the significance of this procedure not only from the theoretical perspective, but also in the practical implementation. We support our claims exhibiting illustrative examples where the absence of the differentiability check in the method prevents the achievement of the minimization problem solution. As possible alternatives, this manuscript presents two procedures that suppress the differentiability check without affecting the convergence of the method (both in theory and in practice). Lastly, by solving a difficult control problem, we show that besides the theoretical appeal our changes may also be useful to address real problems. (AU)

FAPESP's process: 13/14615-7 - On the nonmonotone line search in gradient sampling methods for nonconvex and nonsmooth optimization
Grantee:Lucas Eduardo Azevedo Simões
Support type: Scholarships in Brazil - Doctorate
FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:José Alberto Cuminato
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 13/05475-7 - Computational methods in optimization
Grantee:Sandra Augusta Santos
Support type: Research Projects - Thematic Grants
FAPESP's process: 13/16508-3 - Fast computation of the generalized Backprojection operator with applications in tomographic image reconstruction
Grantee:Elias Salomão Helou Neto
Support type: Regular Research Grants