A Semidefinite Relaxation Scheme for Multivariate Quartic Polynomial Optimization with Quadratic Constraints

Zhi-Quan Luo; Shuzhong Zhang

doi:10.1137/090772952

A Semidefinite Relaxation Scheme for Multivariate Quartic Polynomial Optimization with Quadratic Constraints

SIAM Journal on Optimization ◽

10.1137/090772952 ◽

2010 ◽

Vol 20 (4) ◽

pp. 1716-1736 ◽

Cited By ~ 40

Author(s):

Zhi-Quan Luo ◽

Shuzhong Zhang

Keyword(s):

Polynomial Optimization ◽

Semidefinite Relaxation ◽

Quadratic Constraints ◽

Relaxation Scheme ◽

Quartic Polynomial

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Semidefinite relaxation and new conditions of signdefinitness of quadratic forms under quadratic constraints

2018 14th International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference) (STAB) ◽

10.1109/stab.2018.8408391 ◽

2018 ◽

Cited By ~ 2

Author(s):

L. B. Rapoport

Keyword(s):

Quadratic Forms ◽

Semidefinite Relaxation ◽

Quadratic Constraints

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Semidefinite relaxation method for polynomial optimization with second-order cone complementarity constraints

Journal of Industrial & Management Optimization ◽

10.3934/jimo.2021030 ◽

2017 ◽

Vol 13 (5) ◽

pp. 0-0

Author(s):

Lin Zhu ◽

◽

Xinzhen Zhang

Keyword(s):

Polynomial Optimization ◽

Relaxation Method ◽

Second Order ◽

Semidefinite Relaxation ◽

Complementarity Constraints ◽

Second Order Cone

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Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints

Journal of Global Optimization ◽

10.1007/s10898-010-9545-5 ◽

2010 ◽

Vol 49 (2) ◽

pp. 293-311 ◽

Cited By ~ 13

Author(s):

Xinzhen Zhang ◽

Chen Ling ◽

Liqun Qi

Keyword(s):

Optimization Problems ◽

Quadratic Optimization ◽

Semidefinite Relaxation ◽

Quadratic Constraints

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Semidefinite Relaxation and New Conditions for Sign-Definiteness of the Quadratic Form under Quadratic Constraints

Automation and Remote Control ◽

10.1134/s0005117918110103 ◽

2018 ◽

Vol 79 (11) ◽

pp. 2073-2079 ◽

Cited By ~ 1

Author(s):

L. B. Rapoport

Keyword(s):

Quadratic Form ◽

Semidefinite Relaxation ◽

Quadratic Constraints ◽

Sign Definiteness

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Optimality conditions and optimization methods for quartic polynomial optimization

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.01.074 ◽

2014 ◽

Vol 232 ◽

pp. 968-982 ◽

Cited By ~ 3

Author(s):

Zhiyou Wu ◽

Jing Tian ◽

Jing Quan ◽

Julien Ugon

Keyword(s):

Optimality Conditions ◽

Polynomial Optimization ◽

Optimization Methods ◽

Quartic Polynomial

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Improved approximation results on standard quartic polynomial optimization

Optimization Letters ◽

10.1007/s11590-016-1094-5 ◽

2016 ◽

Vol 11 (8) ◽

pp. 1767-1782 ◽

Cited By ~ 1

Author(s):

Chen Ling ◽

Hongjin He ◽

Liqun Qi

Keyword(s):

Polynomial Optimization ◽

Quartic Polynomial

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Semidefinite Relaxation and New Conditions for Sign-Definiteness of the Quadratic Form under Quadratic Constraints

Автоматика и телемеханика ◽

10.31857/s000523100002779-0 ◽

2018 ◽

pp. 150-158

Author(s):

L. Rapoport

Keyword(s):

Quadratic Form ◽

Semidefinite Relaxation ◽

Quadratic Constraints ◽

Sign Definiteness

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On the triality theory for a quartic polynomial optimization problem

Journal of Industrial & Management Optimization ◽

10.3934/jimo.2012.8.229 ◽

2012 ◽

Vol 8 (1) ◽

pp. 229-242 ◽

Cited By ~ 23

Author(s):

David Yang Gao ◽

◽

Changzhi Wu ◽

Keyword(s):

Optimization Problem ◽

Polynomial Optimization ◽

Polynomial Optimization Problem ◽

Triality Theory ◽

Quartic Polynomial

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Approximation algorithms for homogeneous polynomial optimization with quadratic constraints

Mathematical Programming ◽

10.1007/s10107-010-0409-z ◽

2010 ◽

Vol 125 (2) ◽

pp. 353-383 ◽

Cited By ~ 51

Author(s):

Simai He ◽

Zhening Li ◽

Shuzhong Zhang

Keyword(s):

Approximation Algorithms ◽

Homogeneous Polynomial ◽

Polynomial Optimization ◽

Quadratic Constraints

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Semidefinite relaxation approximation for multivariate bi-quadratic optimization with quadratic constraints

Numerical Linear Algebra with Applications ◽

10.1002/nla.781 ◽

2011 ◽

Vol 19 (1) ◽

pp. 113-131 ◽

Cited By ~ 9

Author(s):

Chen Ling ◽

Xinzhen Zhang ◽

Liqun Qi

Keyword(s):

Quadratic Optimization ◽

Semidefinite Relaxation ◽

Quadratic Constraints

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