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The Proximal Point Algorithm for Pseudo-monotone Operators

Author: ZhouZheng
Tutor: HeYiRan
School: Sichuan Normal University
Course: Operational Research and Cybernetics
Keywords: Pseudomonotone Inexact Proximal Point Algorithm Weak Convergence Strong convergence Relaxation Proximal Point Algorithm Set-valued mapping
CLC: O177.1
Type: Master's thesis
Year: 2010
Downloads: 7
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Abstract


Solodov and Svaiter in 2000 proposed a hybrid approximation algorithm [ 1] , the strong convergence of this method is iterative sequence generated in infinite -dimensional Hilbert space , they use this method to solve the maximal monotone infinite dimensional Hilbert space zero operator is the nature of such a strong convergence will approximate point projection method to two-and-a-half plane contains variational inequalities solution set intersection combination obtained by Tam, Yao and Yen in 2008 proved that in an infinite Inexact Proximal Point Algorithm convergence dimensional space monotone variational inequality is still valid and the second chapter of this paper on the basis of the results , the monotonicity conditions weakened as the pseudo- monotonicity condition in infinite -dimensional Hilbert space proved non accurate approximation point algorithm iteration sequence converges strongly pseudomonotone variational inequalities. classic Proximal Point Algorithm can be used to find the zero of a maximal monotone operator is a known combination Rockafellar research results published in 1976 [23] and concluded Gol'shtein and Tret'yakav in 1979 [ 24] , Eckstein and Bertsekas in 1990 proposed a generalized approximate point algorithm , and use this method to find the Hilbert space maximal monotone operator in a sub- zero [25 ] in reference [ 26 ] this approach has been improved and is used to search for ?? ?? space maximal monotone operator in a given closed convex sub - set within zero in order for this improved relaxation approximation point algorithm gives a new iterative methods for non-precision this this relaxation Proximal point algorithm applied to find ? ? ?? space in the pseudo-monotone set-valued operator proved in a given closed convex subset zero . then in the fourth chapter we will slack approximation algorithm is used to find the pseudo- monotone set-valued operator in infinite dimensional Hilbert space zero iterative sequence generated by the algorithm given in Chapter IV converges strongly pseudo- monotone set-valued operator zero .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Hilbert space and linear operator theory
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