Concepedia

Monotone Operators

Monotone Operators is a mathematical operator in the field of convex analysis characterized by the property that the inner product of the difference between operator values at two points with the difference between the points themselves is nonnegative, thereby generalizing the notion of monotonicity from real-valued functions to set-valued mappings.

2.1K

Publications

116.4K

Citations

2.6K

Authors

1.2K

Institutions

Publications per year

2017–2026

329

Parents

Publications

2.1K

Monotone Operators and the Proximal Point Algorithm

R. T. Rockafellar · SIAM Journal on Control and Optimization · 1976 · 3.6K citations

, , +12

On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators

Jonathan Eckstein, Dimitri P. Bertsekas · Mathematical Programming · 1992 · 2.9K citations · Full text

, , +8

Positive Solutions of Operator Equations.

A. R. Brodsky, M. A. Krasnosel’skii, Richard E. Flaherty et al. · American Mathematical Monthly · 1967 · 2.1K citations

, , +11

Splitting Algorithms for the Sum of Two Nonlinear Operators

Pierre‐Louis Lions, Bertrand Mercier · SIAM Journal on Numerical Analysis · 1979 · 2K citations

, , +8

Polar factorization and monotone rearrangement of vector‐valued functions

Yann Brenier · Communications on Pure and Applied Mathematics · 1991 · 1.7K citations

, , +8

1–5 of 2.1K

Authors

2.6K

  1. WT
    Wataru Takahashi

    Tokyo Institute of Technology, Japan

    28 publications · 4K citations

    22

    h-index

  2. HH
    Heinz H. Bauschke

    University of British Columbia, Okanagan Campus, Canada

    28 publications · 852 citations

    19

    h-index

  3. XW
    Xianfu Wang

    Huazhong University of Science and Technology, China

    21 publications · 635 citations

    17

    h-index

  4. PK
    Poom Kumam

    King Mongkut's University of Technology Thonburi, Thailand

    24 publications · 591 citations

    16

    h-index

  5. BF
    B. F. Svaiter

    Instituto Nacional de Matemática Pura e Aplicada, Brazil

    20 publications · 1.4K citations

    16

    h-index

1–5 of 2.6K

Institutions

1.2K

  1. Tokyo Institute of Technology

    Tokyo, Japan

    21 h-index

    42 publications

    5.5K citations

  2. Centre National de la Recherche Scientifique

    Paris, France

    21 h-index

    55 publications

    3.2K citations

  3. China Medical University

    Taichung, Taiwan

    18 h-index

    35 publications

    1.1K citations

  4. Instituto Nacional de Matemática Pura e Aplicada

    Rio de Janeiro, Brazil

    16 h-index

    31 publications

    1.7K citations

  5. National Sun Yat-sen University

    Kaohsiung City, Taiwan

    16 h-index

    34 publications

    1.7K citations

  6. University of British Columbia

    Vancouver, Canada

    15 h-index

    46 publications

    1.2K citations

  7. King Mongkut's University of Technology Thonburi

    Bangkok, Thailand

    15 h-index

    54 publications

    1.3K citations

  8. Laboratoire Jacques-Louis Lions

    Paris, France

    14 h-index

    16 publications

    2.1K citations

1–8 of 1.2K

Venues

  1. Journal of Mathematical Analysis and Applications

    101 publications · 4.1K citations

    35

    h-index

  2. SIAM Journal on Optimization

    39 publications · 4.8K citations

    31

    h-index

  3. Nonlinear Analysis

    67 publications · 2.9K citations

    28

    h-index

  4. Optimization

    48 publications · 2.3K citations

    25

    h-index

  5. Proceedings of the American Mathematical Society

    PROC · 58 publications · 4K citations

    24

    h-index

1–5