D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 45 Citations 13,750 157 World Ranking 760 National Ranking 28

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Geometry
  • Algebra

His main research concerns Hilbert space, Regular polygon, Mathematical optimization, Subderivative and Combinatorics. He combines subjects such as Projection, Linear subspace, Von Neumann architecture and Monotone polygon with his study of Hilbert space. In his study, Projection is inextricably linked to Fixed point, which falls within the broad field of Regular polygon.

The study incorporates disciplines such as Bregman divergence, Convex function and Convex optimization in addition to Mathematical optimization. His study in Convex optimization is interdisciplinary in nature, drawing from both Fixed-point theorem, Variational analysis and Algorithm, Dykstra's projection algorithm. His Subderivative research includes elements of Convex analysis and Convex set.

His most cited work include:

  • Convex Analysis and Monotone Operator Theory in Hilbert Spaces (2553 citations)
  • On Projection Algorithms for Solving Convex Feasibility Problems (1413 citations)
  • Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization. (428 citations)

What are the main themes of his work throughout his whole career to date?

Pure mathematics, Monotone polygon, Regular polygon, Hilbert space and Monotonic function are his primary areas of study. His Pure mathematics study combines topics from a wide range of disciplines, such as Positive-definite matrix, Convex function, Mathematical analysis and Subderivative. His Subderivative research also works with subjects such as

  • Convex analysis that connect with fields like Mathematical optimization,
  • Convex set that intertwine with fields like Convex hull and Projection.

His Monotone polygon research focuses on Discrete mathematics and how it connects with Pseudo-monotone operator and Strongly monotone. His biological study spans a wide range of topics, including Fixed point, Linear subspace, Combinatorics, Euclidean geometry and Algorithm. His research integrates issues of Intersection, Generalization and Projection in his study of Hilbert space.

He most often published in these fields:

  • Pure mathematics (38.55%)
  • Monotone polygon (32.44%)
  • Regular polygon (32.06%)

What were the highlights of his more recent work (between 2015-2021)?

  • Pure mathematics (38.55%)
  • Regular polygon (32.06%)
  • Monotone polygon (32.44%)

In recent papers he was focusing on the following fields of study:

His primary scientific interests are in Pure mathematics, Regular polygon, Monotone polygon, Convex function and Algorithm. His work carried out in the field of Pure mathematics brings together such families of science as Fixed point, Monotonic function and Subderivative. His Regular polygon research is multidisciplinary, incorporating perspectives in Linear subspace, Projection, Hilbert space, Euclidean geometry and Projector.

The concepts of his Hilbert space study are interwoven with issues in Intersection and Projection. His studies in Monotone polygon integrate themes in fields like Zero, Class, Iterated function and Duality. His Convex function study also includes fields such as

  • Lipschitz continuity that connect with fields like Lemma,
  • Mathematical optimization that intertwine with fields like Convex optimization,
  • Convex set that intertwine with fields like Projection.

Between 2015 and 2021, his most popular works were:

  • A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications (157 citations)
  • On the Douglas---Rachford algorithm (52 citations)
  • Optimal Rates of Linear Convergence of Relaxed Alternating Projections and Generalized Douglas-Rachford Methods for Two Subspaces (38 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Geometry
  • Algebra

His primary areas of investigation include Monotone polygon, Algorithm, Regular polygon, Pure mathematics and Convex function. His study in Monotone polygon is interdisciplinary in nature, drawing from both Fixed point, Numerical analysis and Sequence. His Regular polygon research is multidisciplinary, incorporating elements of Zero, Simple and Euclidean geometry.

Heinz H. Bauschke combines subjects such as Monotonic function and Subderivative with his study of Pure mathematics. His biological study spans a wide range of topics, including Bregman divergence, Convex conjugate, Convex set and Mathematical optimization. His work in Hilbert space is not limited to one particular discipline; it also encompasses Projection.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Heinz H. Bauschke;Patrick L. Combettes.
(2011)

3741 Citations

On Projection Algorithms for Solving Convex Feasibility Problems

Heinz H. Bauschke;Jonathan M. Borwein.
Siam Review (1996)

1692 Citations

Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization.

Heinz H. Bauschke;Patrick L. Combettes;D. Russell Luke.
Journal of The Optical Society of America A-optics Image Science and Vision (2002)

563 Citations

The Approximation of Fixed Points of Compositions of Nonexpansive Mappings in Hilbert Space

Heinz H. Bauschke.
Journal of Mathematical Analysis and Applications (1996)

481 Citations

A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces

Heinz H. Bauschke;Patrick L. Combettes.
Mathematics of Operations Research (2001)

442 Citations

Legendre functions and the method of random Bregman projections

Heinz H. Bauschke;Jonathan M. Borwein.
(1997)

319 Citations

On the convergence of von Neumann's alternating projection algorithm for two sets

Heinz H. Bauschke;Jonathan M. Borwein.
Set-valued Analysis (1993)

274 Citations

Projection and proximal point methods: convergence results and counterexamples

Heinz H. Bauschke;Eva Matoušková;Simeon Reich.
Nonlinear Analysis-theory Methods & Applications (2004)

259 Citations

Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Heinz H. Bauschke;Regina S. Burachik;Patrick L. Combettes;Veit Elser.
(2011)

248 Citations

Bregman Monotone Optimization Algorithms

Heinz H. Bauschke;Jonathan M. Borwein;Patrick L. Combettes.
Siam Journal on Control and Optimization (2003)

242 Citations

Editorial Boards

Journal of Approximation Theory
(Impact Factor: 0.993)

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Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking d-index is inferred from publications deemed to belong to the considered discipline.

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