Taiwanese Journal of Mathematics


Lu-Chuan Ceng and Ching-Feng Wen

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In this paper, we consider a triple hierarchical variational inequality defined over the common solution set of minimization and mixed equilibrium problems. Combining the hybrid steepest-descent method, viscosity approximation method and averaged mapping approach to the gradient-projection algorithm, we propose two iterative methods: implicit one and explicit one, to compute the approximate solutions of our problem. The convergence analysis of the sequences generated by the proposed methods is also established.

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Taiwanese J. Math., Volume 17, Number 4 (2013), 1441-1472.

First available in Project Euclid: 10 July 2017

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Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40] 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 65K05: Mathematical programming methods [See also 90Cxx] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

triple hierarchical variational inequality minimization problem mixed equilibrium problem implicit iterative algorithm explicit iterative algorithm averaged mapping approach


Ceng, Lu-Chuan; Wen, Ching-Feng. HYBRID STEEPEST-DESCENT METHODS FOR TRIPLE HIERARCHICAL VARIATIONAL INEQUALITIES. Taiwanese J. Math. 17 (2013), no. 4, 1441--1472. doi:10.11650/tjm.17.2013.2864. https://projecteuclid.org/euclid.twjm/1499706126

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