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Topic · Computational Theory and Mathematics

Optimization and Variational Analysis

Optimization and Variational Analysis is a research topic within Computational Theory and Mathematics. Science Explorer counts 25k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on iterative algorithms for solving nonlinear operators, optimization problems, fixed-point problems, variational inequalities, and equilibrium problems. It covers convergence theorems, bilevel programming, Hamilton-Jacobi formulations, and the application of nonexpansive mappings in various iterative methods.

  • Iterative Algorithms
  • Nonlinear Operators
  • Optimization
  • Fixed-Point Problems
  • Variational Inequalities
  • Equilibrium Problems
  • Convergence Theorems
  • Bilevel Programming
  • Hamilton-Jacobi Formulation
  • Nonexpansive Mappings
Research works
25k
fractional, since 1950
In the world top 10%
2.5k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+5%
the tick is no change
Largest producer
China
31% of the 10 largest, 2022-now
Optimization and Variational Analysis

Which countries lead Optimization and Variational Analysis research?

By volume, China and India publish the most (690 and 374 works in 2022-now).

By volume, 2022-now

  1. 1 China 690 works
  2. 2 India 374 works
  3. 3 United States 293 works
  4. 4 Russia 162 works
  5. 5 Vietnam 156 works
  6. 6 Germany 118 works
  7. 7 Saudi Arabia 115 works
  8. 8 France 108 works
  9. 9 Iran 104 works
  10. 10 Romania 100 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 31.1%India: 16.9%United States: 13.2%Russia: 7.3%6 others listed: 31.6%31%largest
China690 · 31.1%India374 · 16.9%United States293 · 13.2%Russia162 · 7.3%6 others listed701 · 31.6%

Shares of the rows listed above, not of the whole node.

Which institutions lead Optimization and Variational Analysis research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Optimization and Variational Analysis research, followed by Technion – Israel Institute of Technology and Centre National de la Recherche Scientifique.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 70 works
  2. 2 Technion – Israel Institute of TechnologyIsrael 44 works
  3. 3 Centre National de la Recherche ScientifiqueFrance 40 works
  4. 4 Universitatea Națională de Știință și Tehnologie Politehnica BucureștiRomania 23 works
  5. 5 University of KwaZulu-NatalSouth Africa 22 works
  6. 6 Aligarh Muslim UniversityIndia 22 works
  7. 7 China Medical UniversityTaiwan 21 works
  8. 8 University of DelhiIndia 20 works
  9. 9 University of PhayaoThailand 18 works
  10. 10 Sefako Makgatho Health Sciences UniversitySouth Africa 18 works

Who are the leading researchers in Optimization and Variational Analysis?

The most-cited researchers publishing on Optimization and Variational Analysis include Kai You Wang, Michael I. Jordan and Kalyanmoy Deb.

  1. 1 Kai You Wang China 224k citations
  2. 2 Michael I. Jordan United States 182k citations
  3. 3 Kalyanmoy Deb United States 171k citations
  4. 4 Thomas Brox Germany 145k citations
  5. 5 Stephen Boyd United States 142k citations
  6. 6 Stanley Osher United States 119k citations
  7. 7 Guanrong Chen China 116k citations
  8. 8 Kenneth Joseph Arrow United States 115k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Optimization and Variational Analysis?

The most cited paper in Optimization and Variational Analysis is "Optimal approximations by piecewise smooth functions and associated variational problems" (David B. Mumford, Jayant M. Shah, 1989), with 5,245 citations. Next come "A new approach to variable metric algorithms" (4,132) and "On Nonlinear Fractional Programming" (3,205).

Most cited papers
#PaperReleasedCitations
1 Optimal approximations by piecewise smooth functions and associated variational problems David B. Mumford, Jayant M. Shah · Communications on Pure and Applied Mathematics Open access Jul 1989 5,245
2 A new approach to variable metric algorithms Roger Fletcher · The Computer Journal Mar 1970 4,132
3 On Nonlinear Fractional Programming Werner Dinkelbach · Management Science Mar 1967 3,205
4 On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators Jonathan Eckstein, Dimitri P. Bertsekas · Mathematical Programming Open access Apr 1992 2,923
5 On the stability of the linear mapping in Banach spaces Themistocles M. Rassias · Proceedings of the American Mathematical Society Open access Nov 1978 2,860
All 100 most cited papers, with filters and sorting

Where is Optimization and Variational Analysis research done?

The largest centres of Optimization and Variational Analysis research in 2022-now are Moscow (Russia), Chongqing (China), Hanoi (Vietnam) and Bucharest (Romania). Among places with at least 20 works in it, it is an unusually large share of all research in Aligarh and Haifa.

Largest cities, 2022-now

  1. 1 MoscowRussia 64 works
  2. 2 ChongqingChina 63 works
  3. 3 HanoiVietnam 63 works
  4. 4 BucharestRomania 58 works
  5. 5 BeijingChina 57 works
  6. 6 HaifaIsrael 49 works
  7. 7 ChengduChina 40 works
  8. 8 NanjingChina 39 works
  9. 9 ShanghaiChina 37 works
  10. 10 Ho Chi Minh CityVietnam 37 works

Where it is the local speciality

  1. AligarhIN · 21.7 works19×
  2. HaifaIL · 48.8 works19×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Optimization and Variational Analysis than the world average.

See Optimization and Variational Analysis on the map

Where is the best place to study Optimization and Variational Analysis?

Among universities, judged by research, University of KwaZulu-Natal, Technion – Israel Institute of Technology and University of Phayao score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%30%mean 21.46%fractional works in this field (log) →share of work in the world top 10% →University of KwaZul…Zhejiang Normal Univ…University of PhayaoTechnion – Israel In…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1University of KwaZulu-NatalSouth Africa 72.028.5%18.9×22 -32.7%
2Technion – Israel Institute of TechnologyIsrael 69.412.4%36.5×44 +24.6%
3University of PhayaoThailand 65.122.5%117.1×18 +22.4%
4Zhejiang Normal UniversityChina 63.428.5%18.6×17 +21.8%
5Universitatea Națională de Știință și Tehnologie Politehnica BucureștiRomania 62.920.1%29.5×22 +2.5%
6China Medical UniversityTaiwan 62.224.8%46.4×21 -20.1%
7Banaras Hindu UniversityIndia 55.621.7%6.9×17 +33.0%
8Hanoi University of Science and TechnologyVietnam 55.024.6%20.4×12 +20.6%
9King Abdulaziz UniversitySaudi Arabia 54.713.0%8.6×15 +36.3%
10Wayne State UniversityUnited States 53.718.5%9.8×11 +64.3%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Optimization and Variational Analysis, country by country

Is Optimization and Variational Analysis research growing?

Output in 2022-2025 was 5% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Optimization and Variational Analysis.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Optimization and Variational Analysis as a percentage of every work published that year, 0.014% in 2024.

still counting0.020%0.040%0.060%Optimization and Variational Analysis0.015% in 202519801990200020102020

Fractional works of Optimization and Variational Analysis over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Optimization and Variational Analysis10.2% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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