Hybrid Steepest Descent Method for Variational Inequality Problem over the Fixed Point Set of Certain Quasi-nonexpansive Mappings

By Isao Yamada, Nobuhiko Ogura. 2005

296 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d8bae8b4f26de05754111e9e7095016bba104000

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Aviv Gibali
2. Simeon Reich
3. Yekini Shehu
4. Patrick L. Combettes
5. Dang Van Hieu
6. Duong Viet Thong
7. Isao Yamada
8. Heinz H. Bauschke

In Geometry and Topology

1. Simeon Reich
2. Aviv Gibali
3. Patrick L. Combettes
4. Heinz H. Bauschke
5. Rafał Zalas
6. Isao Yamada
7. Andrzej Cegielski
8. Paul-Emile Maingé

In Numerical Analysis

1. Aviv Gibali
2. Simeon Reich
3. Yekini Shehu
4. Patrick L. Combettes
5. Dang Van Hieu
6. Satit Saejung
7. Rapeepan Kraikaew
8. Duong Viet Thong

Citations in the corpus

• Adaptive Projected Subgradient Method for Asymptotic Minimization of Sequence of Nonnegative Convex Functions (2005, background): “Proposition 1 (Selected properties of quasi-nonexpansive mappings, Yamada and Ogura, 2004).”
• Perturbed projections and subgradient projections for the multiple-sets split feasibility problem (2007, background): “…includes, among many oth-Y ers, the works of Crombez [18,19], the connection with variational inequalities, see, e.g., Aslam Noor [21], Yamada’s [27] which is motivated by real-world problems of signal processing, and the many contributions of Bauschke and Combettes, see, e.g., Bauschke,…”
• Outer approximation methods for solving variational inequalities in Hilbert space (2017, methodology): “On the other hand, the HSD method for more general F has been investigated by Yamada [21], Xu and Kim [22], Yamada and Ogura [23], Hirstoaga [24], Zeng et al. [25], Yamada and Takahashi [26], Aoyama and Kimura [27], Zhang and He [28], Cegielski and Zalas [29], Aoyama and Kohsaka [30], Zalas [31], Ce”
• Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces (2007, background): “It is well known that S is a closed convex set of D (see for instance [14]).”
• Convergence theorems for inertial KM-type algorithms (2008, background): “It is well known that Fix(Ti )= arg minKi i , and that Ti ∈ EN for i ∈ (0, 2/ i] [20,21].”
• Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces (2014, background): “Many problems in science and engineering can be recast as variational inequalities (see, for example, [1–8]).”