Construction of best Bregman approximations in reflexive Banach spaces

By Heinz H. Bauschke, Patrick L. Combettes. 2003

69 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/2a253a2bc16506cdc75aea594729737db4a430c0

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. Simeon Reich
2. Aviv Gibali
3. Shoham Sabach
4. Patrick L. Combettes
5. Yair Censor
6. Heinz H. Bauschke
7. Jonathan Michael Borwein
8. Yekini Shehu

In Geometry and Topology

1. Simeon Reich
2. Shoham Sabach
3. Jonathan Michael Borwein
4. Patrick L. Combettes
5. Heinz H. Bauschke
6. Aviv Gibali
7. Yair Censor
8. Qamrul Hasan Ansari

In Numerical Analysis

1. Simeon Reich
2. Aviv Gibali
3. Shoham Sabach
4. Yair Censor
5. Patrick L. Combettes
6. Heinz H. Bauschke
7. Jonathan Michael Borwein
8. Qamrul Hasan Ansari

Citations in the corpus

• Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces (2006, unknown): “Iterative algorithms for computing Bregman projections on more general sets are presented in [15].”
• A projection method for solving nonlinear problems in reflexive Banach spaces (2011, background): “Other algorithms which can be applied to BFNE operators can be found, for example, in [6, 24, 25].”
• Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space (2011, background): “[2] H.H. Bauschke and P.L. Combettes, A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces, Math.”
• Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces (2010, background): “They also differ from the algorithm in [6] in the definition of the sets Cn and in our taking into account possible computational errors.”
• Bregman Monotone Optimization Algorithms (2003, methodology): “The tools developed in this paper also provide the main building blocks for the algorithms proposed in [10] to find best Bregman approximations from intersections of closed convex sets in reflexive Banach spaces.”
• MANN TYPE HYBRID EXTRAGRADIENT METHOD FOR VARIATIONAL INEQUALITIES, VARIATIONAL INCLUSIONS AND FIXED POINT PROBLEMS (2012, methodology): “16 (4) (2006) 1230-1241] introduced an iterative algorithm for finding a common element of the fixed point set of a nonexpansive mapping and the solution set of a variational inequality in a real Hilbert space via combining two well-known methods: hybrid and extragradient.”
• A Characterization of Bregman Firmly Nonexpansive Operators Using a New Monotonicity Concept (2011, background): “See, for instance, [2, 3, 4, 5, 6, 13, 12, 7, 14, 15, 17, 20, 21, 22, 23, 24] and the references therein.”