A hybrid steepest-descent method for variational inequalities in Hilbert spaces

DOI10.1080/00036810802140608zbMath1158.47050OpenAlexW1968854694WikidataQ58259004 ScholiaQ58259004MaRDI QIDQ3518693

Hong-Kun Xu, Lu-Chuan Ceng, Jen-Chih Yao

Publication date: 11 August 2008

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810802140608

zbMATH Keywords

convergence analysisstrong convergencevariational inequalityHilbert spaceMann-type hybrid steepest-descent methoddemiclosedness principlenon-expansive mappings

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Hybrid steepest-descent methods with a countable family of nonexpansive mappings for variational inequalities in Hilbert spaces, An improved algorithm with Armijo line-search rule for solving pseudomonotone variational inequality problems in Banach spaces, Existence theorems for generalized set-valued mixed (quasi-)variational inequalities in Banach spaces, Explicit hierarchical fixed point approach to variational inequalities, A new iterative method for solving equilibrium problems and fixed point problems for infinite family of nonexpansive mappings, Unnamed Item, Regularization and iterative methods for monotone variational inequalities, A generalized hybrid steepest-descent method for variational inequalities in Banach spaces, A new hybrid algorithm for variational inclusions, generalized equilibrium problems, and a finite family of quasi-nonexpansive mappings

Cites Work

• Convergence of hybrid steepest-descent methods for variational inequalities
• Variational inequalities and the pricing of American options
• Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces
• Convergence analysis of modified hybrid steepest-descent methods with variable parameters for variational inequalities
• An iterative approach to quadratic optimization
• Viscosity approximation methods for nonexpansive mappings
• An extragradient-like approximation method for variational inequality problems and fixed point problems
• Convergence of hybrid steepest-descent methods for generalized variational inequalities
• Iterative Algorithms for Nonlinear Operators
• Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings