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Advanced Optimization Algorithms Research

Advanced Optimization Algorithms Research is a research topic within Numerical Analysis. Science Explorer counts 30k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers advances in numerical optimization techniques, including topics such as benchmarking optimization software, semidefinite programming, global optimization, derivative-free optimization, and the application of sum of squares techniques. It also explores interior-point methods, quadratic programming, and mixed-integer nonlinear programs.

  • Optimization Software
  • Semidefinite Programming
  • Global Optimization
  • Nonlinear Programming
  • Interior-Point Methods
  • Derivative-Free Optimization
  • Quadratic Programming
  • Convex Optimization
  • Mixed-Integer Nonlinear Programs
  • Sum of Squares Techniques
Research works
30k
fractional, since 1950
In the world top 10%
2.9k
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+7%
the tick is no change
Largest producer
China
37% of the 10 largest, 2022-now
Advanced Optimization Algorithms Research

Which countries lead Advanced Optimization Algorithms Research research?

By volume, China and the United States publish the most (1k and 572 works in 2022-now).

By volume, 2022-now

  1. 1 China 1k works
  2. 2 United States 572 works
  3. 3 India 296 works
  4. 4 Germany 190 works
  5. 5 France 145 works
  6. 6 Russia 127 works
  7. 7 Iran 109 works
  8. 8 Italy 108 works
  9. 9 Vietnam 106 works
  10. 10 Japan 95 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: 37.1%United States: 20.6%India: 10.6%Germany: 6.8%6 others listed: 24.9%37%largest
China1,031 · 37.1%United States572 · 20.6%India296 · 10.6%Germany190 · 6.8%6 others listed691 · 24.9%

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

Which institutions lead Advanced Optimization Algorithms Research research?

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

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 53 works
  2. 2 Russian Academy of SciencesRussia 37 works
  3. 3 Technion – Israel Institute of TechnologyIsrael 32 works
  4. 4 Chinese Academy of SciencesChina 23 works
  5. 5 Georgia Institute of TechnologyUnited States 22 works
  6. 6 Guangxi UniversityChina 21 works
  7. 7 University of MosulIraq 21 works
  8. 8 Sapienza University of RomeItaly 19 works
  9. 9 Cameron UniversityUnited States 18 works
  10. 10 Universitat Politècnica de ValènciaSpain 17 works

Who are the leading researchers in Advanced Optimization Algorithms Research?

The most-cited researchers publishing on Advanced Optimization Algorithms Research include Trevor Hastie, Xiaogang Wang and Gordon K. Smyth.

  1. 1 Trevor Hastie United States 301k citations
  2. 2 Xiaogang Wang China 260k citations
  3. 3 Gordon K. Smyth Australia 237k citations
  4. 4 Kai You Wang China 224k citations
  5. 5 Michael I. Jordan United States 182k 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 Advanced Optimization Algorithms Research?

The most cited paper in Advanced Optimization Algorithms Research is "Adam: A Method for Stochastic Optimization" (Mandi, Jayanta, Canoy, Rocsildes, Bucarey, Víctor et al., 2015), with 50,327 citations. Next come "No free lunch theorems for optimization" (14,318) and "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming" (9,722).

Most cited papers
#PaperReleasedCitations
1 Adam: A Method for Stochastic Optimization Mandi, Jayanta, Canoy, Rocsildes, Bucarey, Víctor et al. · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) Open access May 2015 50,327
2 No free lunch theorems for optimization David H. Wolpert, William G. Macready · IEEE Transactions on Evolutionary Computation Apr 1997 14,318
3 On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Andreas Wächter, Lorenz T. Biegler · Mathematical Programming 28 Apr 2005 9,722
4 YALMIP : a toolbox for modeling and optimization in MATLAB Johan Löfberg Conference paper 21 Mar 2005 9,338
5 On the limited memory BFGS method for large scale optimization Dong C. Liu, Jorge Nocedal · Mathematical Programming Aug 1989 8,813
All 100 most cited papers, with filters and sorting

Where is Advanced Optimization Algorithms Research research done?

The largest centres of Advanced Optimization Algorithms Research research in 2022-now are Beijing (China), Shanghai (China), Chongqing (China) and Moscow (Russia).

Largest cities, 2022-now

  1. 1 BeijingChina 119 works
  2. 2 ShanghaiChina 76 works
  3. 3 ChongqingChina 55 works
  4. 4 MoscowRussia 47 works
  5. 5 NanjingChina 45 works
  6. 6 ParisFrance 43 works
  7. 7 HanoiVietnam 43 works
  8. 8 TokyoJapan 42 works
  9. 9 Xi'anChina 42 works
  10. 10 BucharestRomania 38 works
See Advanced Optimization Algorithms Research on the map

Where is the best place to study Advanced Optimization Algorithms Research?

Among universities, judged by research, Guangxi University, University of KwaZulu-Natal and Technion – Israel Institute of Technology 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%20%40%mean 20.13%fractional works in this field (log) →share of work in the world top 10% →Guangxi UniversityUniversity of KwaZul…Massachusetts Instit…Technion – 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
1Guangxi UniversityChina 71.328.1%9.3×21 +29.9%
2University of KwaZulu-NatalSouth Africa 69.526.8%11.7×16 -29.1%
3Technion – Israel Institute of TechnologyIsrael 64.18.7%22.6×32 +8.2%
4Massachusetts Institute of TechnologyUnited States 62.826.7%4.6×12 +18.3%
5Georgia Institute of TechnologyUnited States 61.111.7%9.5×22 +43.0%
6Hong Kong Polytechnic UniversityChina 58.915.4%4.5×14 +53.4%
7Zhejiang Normal UniversityChina 56.920.7%13.3×14 +38.7%
8China Medical UniversityTaiwan 56.929.0%21.5×11 -33.9%
9Lehigh UniversityUnited States 56.218.0%28.9×13 +130.5%
10Universitat Politècnica de ValènciaSpain 55.716.2%13.1×18 -3.6%

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 Advanced Optimization Algorithms Research, country by country

Is Advanced Optimization Algorithms Research research growing?

Output in 2022-2025 was 7% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Advanced Optimization Algorithms Research.

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 Advanced Optimization Algorithms Research as a percentage of every work published that year, 0.018% in 2024.

still counting0.020%0.040%0.060%Advanced Optimization Algorithms Research0.018% in 202519801990200020102020

Fractional works of Advanced Optimization Algorithms Research 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%Advanced Optimization Algorithms Research9.9% 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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