Amoebas, nonnegative polynomials and sums of squares supported on circuits

Article Properties
Journal Category
Science
Mathematics
Refrences
Title Journal Journal Categories Citations Publication Date
NP-hardness of deciding convexity of quartic polynomials and related problems Mathematical Programming
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software
  • Technology: Manufactures: Production management. Operations management
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
 58 2013
Convex normality of rational polytopes with long edges Advances in Mathematics
  • Science: Mathematics
 14 2012
Discriminants and nonnegative polynomials Journal of Symbolic Computation
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
  • Technology: Engineering (General). Civil engineering (General)
  • Technology: Engineering (General). Civil engineering (General)
 26 2012
Lower Bounds for Polynomials Using Geometric Programming SIAM Journal on Optimization
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 14 2012
Positive semidefinite diagonal minus tail forms are sums of squares Mathematische Zeitschrift
  • Science: Mathematics
 16 2011
Citations
Title Journal Journal Categories Citations Publication Date
Real tropicalization and negative faces of the Newton polytope Journal of Pure and Applied Algebra
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 2024
Weighted Geometric Mean, Minimum Mediated Set, and Optimal Simple Second-Order Cone Representation SIAM Journal on Optimization
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 2024
Learning variational models with unrolling and bilevel optimization

 Analysis and Applications
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 2024
Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks

 Mathematical Programming
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software
  • Technology: Manufactures: Production management. Operations management
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
 2023
A Survey on Computational Aspects of Polynomial Amoebas Mathematics in Computer Science
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
 1 2023
Citations Analysis
Category Category Repetition
Science: Mathematics31
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods29
Science: Mathematics: Instruments and machines: Electronic computers. Computer science10
Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software4
Technology: Manufactures: Production management. Operations management4
Technology: Engineering (General). Civil engineering (General)4
Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics: Computer engineering. Computer hardware2
The category Science: Mathematics 31 is the most commonly referenced area in studies that cite this article. The first research to cite this article was titled Lower Bounds for Polynomials with Simplex Newton Polytopes Based on Geometric Programming and was published in 2016. The most recent citation comes from a 2024 study titled Weighted Geometric Mean, Minimum Mediated Set, and Optimal Simple Second-Order Cone Representation. This article reached its peak citation in 2021, with 8 citations. It has been cited in 18 different journals. Among related journals, the SIAM Journal on Optimization cited this research the most, with 5 citations. The chart below illustrates the annual citation trends for this article.
Citations used this article by year