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- W2028594032 abstract "We consider the general variational inequality GVI ( F , g , C ) , where F and g are mappings from a Hilbert space into itself and C is intersection of the fixed point sets of a finite family of nonexpansive mappings. We suggest and analyze an iterative algorithm with variable parameters as follows: u n + 1 = ( 1 − α n + 1 + θ n + 1 ) T [ n + 1 ] u n + α n + 1 u n − θ n + 1 g ( T [ n + 1 ] u n ) − λ n + 1 μ n + 1 F ( T [ n + 1 ] u n ) , n ⩾ 0 . The sequence { u n } is shown to converge in norm to the solutions of the general variational inequality GVI ( F , g , C ) under some mild conditions. Application to constrained generalized pseudo-inverse is included. Since the general variational inequalities include variational inequalities, quasi-variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as a refinement and improvement of the previously known results." @default.
- W2028594032 created "2016-06-24" @default.
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- W2028594032 date "2007-10-01" @default.
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- W2028594032 title "On modified hybrid steepest-descent methods for general variational inequalities" @default.
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- W2028594032 doi "https://doi.org/10.1016/j.jmaa.2007.01.036" @default.
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