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General models for the relaxed proximal point algorithm using the notion of relative maximal accretiveness (RMA) are developed,and then the convergence analysis for these models in the context of solving a general class of nonlinear inclusion problems differs significantly than that of Rockafellar (1976), where the local Lipschitz continuity at zero is adopted instead. Moreover, our approach not only generalizes convergence results to real Banach space settings, but also provides a suitable alternative to other problems arising from other related fields.
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참고문헌 (24)
참고문헌 신청
A. Moudafi / 2002 / Mixed equilibrium problems: sensitivity analysis and algorithmic aspect / Comput. Math. Appl. 44 (8) : 1099 ~ 1108
B. Martinet / 1970 / R´egularisation d’in´equations variationnelles par approximations successives, Rev. Francaise Inform / Rech. Oper. Ser. R-3 : 154 ~ 158
H. Y. Lan / 2007 / On a new system of nonlinear A-monotone multivalued variational inclusions / J. Math. Anal. Appl. 327 (1) : 481 ~ 493
J. Eckstein / 1992 / On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators / Math. Programming 55 (3) : 293 ~ 318
M. Fukushima / 1996 / The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem / Math. Programming
B. Martinet / 1970 / R´egularisation d’in´equations variationnelles par approximations successives, Rev. Francaise Inform / Rech. Oper. Ser. R-3 : 154 ~ 158
H. Y. Lan / 2007 / On a new system of nonlinear A-monotone multivalued variational inclusions / J. Math. Anal. Appl. 327 (1) : 481 ~ 493
J. Eckstein / 1992 / On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators / Math. Programming 55 (3) : 293 ~ 318
M. Fukushima / 1996 / The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem / Math. Programming
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