Robustness of the Hybrid Extragradient Proximal-Point Algorithm

R. S. Burachik, S. Scheimberg and B. F. Svaiter
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R. S. Burachik: Universidade Federal do Rio de Janeiro
S. Scheimberg: Universidade Federal do Rio de Janeiro
B. F. Svaiter: Instituto de Matemática Pura e Aplicada

Journal of Optimization Theory and Applications, 2001, vol. 111, issue 1, No 6, 117-136

Abstract: Abstract The hybrid extragradient proximal-point method recently proposed by Solodov and Svaiter has the distinctive feature of allowing a relative error tolerance. We extend the error tolerance of this method, proving that it converges even if a summable error is added to the relative error. Furthermore, the extragradient step may be performed inexactly with a summable error. We present a convergence analysis, which encompasses other well-known variations of the proximal-point method, previously unrelated. We establish weak global convergence under mild assumptions.

Keywords: Maximal monotone operators; proximal-point algorithm; extragradient method; enlargement of a maximal monotone operator (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (4)

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DOI: 10.1023/A:1017523331361

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