Relaxed proximal point algorithms based on A-maximal relaxed monotonicity frameworks with applications
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Abstract. Based on the A-maximal (m)-relaxed monotonicity frame-works, the approximation solvability of a general class of variational in-clusion problems using the relaxed proximal point algorithm is explored,while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modi ed version of the relaxed proximal point al-gorithm, Eckstein and Bertsekas (1992) on weak convergence using the relaxed proximal point algorithm to the context of the Douglas-Rachford splitting method, and Rockafellar (1976) on weak as well as strong con-vergence results on proximal point algorithms in real Hilbert space set-tings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of vari-ational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to rst-order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for nding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.
Abstract
Abstract. Based on the A-maximal (m)-relaxed monotonicity frame-works, the approximation solvability of a general class of variational in-clusion problems using the relaxed proximal point algorithm is explored,while generalizing most of the investigations, especially of Xu (2002) on strong convergence of modi ed version of the relaxed proximal point al-gorithm, Eckstein and Bertsekas (1992) on weak convergence using the relaxed proximal point algorithm to the context of the Douglas-Rachford splitting method, and Rockafellar (1976) on weak as well as strong con-vergence results on proximal point algorithms in real Hilbert space set-tings. Furthermore, the main result has been applied to the context of the H-maximal monotonicity frameworks for solving a general class of vari-ational inclusion problems. It seems the obtained results can be used to generalize the Yosida approximation that, in turn, can be applied to rst-order evolution inclusions, and can also be applied to Douglas-Rachford splitting methods for nding the zero of the sum of two A-maximal (m)-relaxed monotone mappings.
참고문헌 (15)
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