Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 17, Number 4 (2013), 1441-1472.
HYBRID STEEPEST-DESCENT METHODS FOR TRIPLE HIERARCHICAL VARIATIONAL INEQUALITIES
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.
Taiwanese J. Math., Volume 17, Number 4 (2013), 1441-1472.
First available in Project Euclid: 10 July 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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.
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