Robustness of the Hybrid Extragradient Proximal-Point Algorithm |
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Authors: | Burachik R S Scheimberg S Svaiter B F |
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Institution: | (1) Engenharia de Sistemas e Computação, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;(2) Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;(3) Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil |
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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. |
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Keywords: | Maximal monotone operators proximal-point algorithm extragradient method enlargement of a maximal monotone operator |
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