Optimality conditions and finite convergence of Lasserre’s hierarchy J Nie Mathematical programming 146, 97-121, 2014 | 284 | 2014 |

Semidefinite representation of convex sets JW Helton, J Nie Mathematical Programming 122, 21-64, 2010 | 238 | 2010 |

On the complexity of Putinar's Positivstellensatz J Nie, M Schweighofer Journal of Complexity 23 (1), 135-150, 2007 | 213 | 2007 |

Minimizing polynomials via sum of squares over the gradient ideal J Nie, J Demmel, B Sturmfels Mathematical programming 106, 587-606, 2006 | 197 | 2006 |

All real eigenvalues of symmetric tensors CF Cui, YH Dai, J Nie SIAM Journal on Matrix Analysis and Applications 35 (4), 1582-1601, 2014 | 150 | 2014 |

Biquadratic optimization over unit spheres and semidefinite programming relaxations C Ling, J Nie, L Qi, Y Ye SIAM Journal on Optimization 20 (3), 1286-1310, 2010 | 145 | 2010 |

The algebraic degree of semidefinite programming J Nie, K Ranestad, B Sturmfels Mathematical Programming 122, 379-405, 2010 | 144 | 2010 |

Sum of squares method for sensor network localization J Nie Computational Optimization and Applications 43 (2), 151-179, 2009 | 137 | 2009 |

Semidefinite relaxations for best rank-1 tensor approximations J Nie, L Wang SIAM Journal on Matrix Analysis and Applications 35 (3), 1155-1179, 2014 | 130 | 2014 |

Sufficient and necessary conditions for semidefinite representability of convex hulls and sets JW Helton, J Nie SIAM Journal on Optimization 20 (2), 759-791, 2009 | 123 | 2009 |

Certifying convergence of Lasserre’s hierarchy via flat truncation J Nie Mathematical Programming 142, 485-510, 2013 | 113 | 2013 |

Semidefinite relaxation bounds for indefinite homogeneous quadratic optimization S He, ZQ Luo, J Nie, S Zhang SIAM Journal on Optimization 19 (2), 503-523, 2008 | 109 | 2008 |

The A-Truncated K-Moment Problem J Nie Foundations of Computational Mathematics 14 (6), 1243-1276, 2014 | 102 | 2014 |

An exact Jacobian SDP relaxation for polynomial optimization J Nie Mathematical Programming 137, 225-255, 2013 | 85 | 2013 |

Algebraic degree of polynomial optimization J Nie, K Ranestad SIAM Journal on Optimization 20 (1), 485-502, 2009 | 77 | 2009 |

Semidefinite Representation of the *k*-EllipseJ Nie, PA Parrilo, B Sturmfels Algorithms in algebraic geometry, 117-132, 2008 | 76 | 2008 |

Positivity of Riesz functionals and solutions of quadratic and quartic moment problems L Fialkow, J Nie Journal of Functional Analysis 258 (1), 328-356, 2010 | 73 | 2010 |

Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals J Demmel, J Nie, V Powers Journal of pure and applied algebra 209 (1), 189-200, 2007 | 72 | 2007 |

Addressing the needs of complex MEMS design JV Clark, D Bindel, W Kao, E Zhu, A Kuo, N Zhou, J Nie, J Demmel, Z Bai, ... Technical Digest. MEMS 2002 IEEE International Conference. Fifteenth IEEE …, 2002 | 70 | 2002 |

Generating polynomials and symmetric tensor decompositions J Nie Foundations of Computational Mathematics 17, 423-465, 2017 | 64 | 2017 |