Semidefinite representation of convex sets JW Helton, J Nie Mathematical Programming 122 (1), 21-64, 2010 | 175 | 2010 |

Optimality conditions and finite convergence of Lasserre’s hierarchy J Nie Mathematical programming 146 (1), 97-121, 2014 | 168 | 2014 |

Minimizing polynomials via sum of squares over the gradient ideal J Nie, J Demmel, B Sturmfels Mathematical programming 106 (3), 587-606, 2006 | 163 | 2006 |

On the complexity of Putinar's Positivstellensatz J Nie, M Schweighofer Journal of Complexity 23 (1), 135-150, 2007 | 143 | 2007 |

Sum of squares method for sensor network localization J Nie Computational Optimization and Applications 43 (2), 151-179, 2009 | 122 | 2009 |

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 | 114 | 2010 |

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 | 111 | 2009 |

The algebraic degree of semidefinite programming J Nie, K Ranestad, B Sturmfels Mathematical Programming 122 (2), 379-405, 2010 | 104 | 2010 |

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 | 99 | 2008 |

Semidefinite relaxations for best rank-1 tensor approximations J Nie, L Wang SIAM Journal on Matrix Analysis and Applications 35 (3), 1155-1179, 2014 | 95 | 2014 |

All real eigenvalues of symmetric tensors CF Cui, YH Dai, J Nie SIAM Journal on Matrix Analysis and Applications 35 (4), 1582-1601, 2014 | 90 | 2014 |

Certifying convergence of Lasserre’s hierarchy via flat truncation J Nie Mathematical Programming 142 (1), 485-510, 2013 | 69 | 2013 |

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 | 67 | 2002 |

An exact Jacobian SDP relaxation for polynomial optimization J Nie Mathematical Programming 137 (1), 225-255, 2013 | 64 | 2013 |

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 | 60 | 2010 |

Semidefinite Representation of the *k*-EllipseJ Nie, PA Parrilo, B Sturmfels Algorithms in algebraic geometry, 117-132, 2008 | 58 | 2008 |

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 | 55 | 2007 |

The A -Truncated K -Moment Problem J Nie Foundations of Computational Mathematics 14 (6), 1243-1276, 2014 | 54 | 2014 |

Regularization methods for SDP relaxations in large-scale polynomial optimization J Nie, L Wang SIAM Journal on Optimization 22 (2), 408-428, 2012 | 49* | 2012 |

Discriminants and nonnegative polynomials J Nie Journal of Symbolic Computation 47 (2), 167-191, 2012 | 48 | 2012 |