Taiwanese Journal of Mathematics

HYBRID STEEPEST-DESCENT METHODS FOR TRIPLE HIERARCHICAL VARIATIONAL INEQUALITIES

Lu-Chuan Ceng and Ching-Feng Wen

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706126

Digital Object Identifier
doi:10.11650/tjm.17.2013.2864

Mathematical Reviews number (MathSciNet)
MR3085520

Zentralblatt MATH identifier
1276.49005

Subjects
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.

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

Citation

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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References

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