Abstract
A proximal linearized algorithm for minimizing difference of two convex functions is proposed. If the sequence generated by the algorithm is bounded it is proved that every cluster point is a critical point of the function under consideration, even if the auxiliary minimizations are performed inexactly at each iteration. Linear convergence of the sequence is established under suitable additional assumptions.
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The authors wish to express their gratitude to the anonymous referees for them helpful comments.
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The research of the J. C. Souza was supported in part by CNPq-Ciências sem Fronteiras Grant 203360/2014-1. The P. R. Oliveira was partially supported by CNPq, Brazil.
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Souza, J.C.O., Oliveira, P.R. & Soubeyran, A. Global convergence of a proximal linearized algorithm for difference of convex functions. Optim Lett 10, 1529–1539 (2016). https://doi.org/10.1007/s11590-015-0969-1
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DOI: https://doi.org/10.1007/s11590-015-0969-1