A Convex Form That Is Not a Sum of Squares
Published Online:28 Jul 2022https://doi.org/10.1287/moor.2022.1273
References
- [1] (2013) A complete characterization of the gap between convexity and SOS-convexity. SIAM J. Optim. 23(2):811–833.Crossref, Google Scholar
- [2] (2019) Polynomial norms. SIAM J. Optim. 29(1):399–422.Crossref, Google Scholar
- [3] (2017) Sum-of-squares certificates for maxima of random tensors on the sphere. Jansen K, Rolim JDP, Williamson D, Vempala SS, eds. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, vol. 81 (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany), 31:1–31:20.Google Scholar
- [4] (2012) Nonnegative polynomials and sums of squares. Semidefinite Optimization and Convex Algebraic Geometry (SIAM, Philadelphia), 159–202.Crossref, Google Scholar
- [5] (2002) Approximation of the stability number of a graph via copositive programming. SIAM J. Optim. 12(4):875–892.Crossref, Google Scholar
- [6] (1994) On the eigenvalues of random matrices. J. Appl. Probability 31(A):49–62.Crossref, Google Scholar
- [7] (2020) On sum of squares representation of convex forms and generalized Cauchy–Schwarz inequalities. SIAM J. Appl. Algebra Geometry 4(2):377–400.Crossref, Google Scholar
- [8] (2021) The sum-of-squares hierarchy on the sphere and applications in quantum information theory. Math. Programming (Springer), 190(1):331–360.Crossref, Google Scholar
- [9] (1981) Cliffordalgebren und neue isoparametrische Hyperflächen. Math. Z 177(4):479–502.Crossref, Google Scholar
- [10] (1878) Über lineare Substitutionen und bilineare Formen. J. Reine Angewandte Mathematik 1878(84):1–63.Google Scholar
- [11] (2004) Symmetry groups, semidefinite programs, and sums of squares. J. Pure Appl. Algebra 192(1-3):95–128.Crossref, Google Scholar
- [12] (2018) Isoparametric polynomials and sums of squares. Preprint, submitted November 13, https://arxiv.org/abs/1811.05587.Google Scholar
- [13] (2016) On the Choi–Lam analogue of Hilbert’s 1888 theorem for symmetric forms. Linear Algebra Appl. 496:114–120.Crossref, Google Scholar
- [14] (1990) Spinors and Calibrations (Elsevier, New York).Google Scholar
- [15] (2010) Semidefinite representation of convex sets. Math. Programming 122(1):21–64.Crossref, Google Scholar
- [16] (1888) Über die Darstellung definiter Formen als Summe von Formenquadraten. Math. Ann. 32(3):342–350.Crossref, Google Scholar
- [17] (1898) Ueber die Composition der quadratischen Formen von belibig vielen Variablen (Nach. Ges. Wiss, Göttingen).Google Scholar
- [18] (2014) Nonnegative polynomials and sums of squares: Boundary structure, symmetries and sparsity. PhD thesis, Goethe-Universität, Frankfurt, Germany.Google Scholar
- [19] (1998) Octonion hermitian quadrangles. Bull. Belgium Math. Soc. Simon Stevin 5(2/3):353–362.Google Scholar
- [20] (1965) Maxima for graphs and a new proof of a theorem of Turán. Canadian J. Math. 17:533–540.Crossref, Google Scholar
- [21] (2012) Sum of squares methods for minimizing polynomial forms over spheres and hypersurfaces. Frontiers Math. China 7(2):321–346.Crossref, Google Scholar
- [22] (1975) On some types of isoparametric hypersurfaces in spheres I. Tohoku Math. J. 27(4):515–559.Crossref, Google Scholar
- [23] (2012) Polynomial optimization, sums of squares, and applications. Semidefinite Optimization and Convex Algebraic Geometry (SIAM, Philadelphia), 47–157.Crossref, Google Scholar
- [24] (2004) On the moments of traces of matrices of classical groups. Comm. Math. Phys. 252(1):149–166.Crossref, Google Scholar
- [25] (2018) Symmetric sums of squares over k-subset hypercubes. Math. Programming 167(2):315–354.Crossref, Google Scholar
- [26] (1901) Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen (Dieterich).Google Scholar
- [27] (2005) On the Diaconis-Shahshahani method in random matrix theory. J. Algebraic Combinations 22(4):471–491.Crossref, Google Scholar
- [28] (2000) Matrix representations of octonions and their applications. Adv. Appl. Clifford Algebra 1(10):61–90.Crossref, Google Scholar

